For each of the following quadratic equations, determine the number and the nature of the roots by first calculating the quadratic's discriminant.

Q: Find the roots of 2x2-2(√2x) +1=0,If they  exist using quadratic formula

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Q: Find a quadratic equation whose product of roots x, and x₂ is X₂ equal to 4 and satisfying the…

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Q: If the roots of x²-ax+b=0 is twice the other.find b in terms of a

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Q: If a and 3 are the roots of the quadratic 3r² – 4.x + 6 = 0, find the value of ( + )

A: We have to solve given problem:

Q: Use the quadratic formula to find the roots following quadratic: y = x² + 4x +5

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Q: Find the roots of each of the following quadratic equations. 1. 4x^2 + 12x - 16 = 0 2. 2x^2 + 17x +…

A: We need to find roots.

Q: For the following quadratic equation, find the discriminant. -6x² + 12x + 12 = –7x² – 2 %3D Answer:…

A: ax^2+bx+c=0 Discriminant =b^2-4ac

Q: Find the formula, in standard form y=ax2+bx+c, for a quadratic that has roots at x = 5 and x= -1,…

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Q: Determine the number of roots that each of the following quadratic relations has. (hint: DO NOT…

A: We have to check

Q: If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the…

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Q: If the roots of the equation a(b - c)x² +b(c - a)x + c (a - b)=0 2 _ 1 ,1. are equal, show that а с

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Q: For the following quadratic equation, find the discriminant. 4x2 + 107x + 313 = -x² + 7x – 7 %3D…

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Q: Which of the following equations is a quadratic equation? O 2x° = (2x2 – 1) (3x + 4) %3D O 14x (x…

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Q: For the following quadratic equation, find the discriminant. 4x + 107x + 313 = -x² + 7x – 7 ,2

A: Take all terms in right side and then compare it with standard equation

Q: Solve for the range and axis of symmetry of the given quadratic functions

A: To Solve for the range and axis of symmetry of the given quadratic functions4) y=x2+5x-145)…

Q: Given that each of the following quadratic equations has no real roots, find the Pange of kx² - 4x +…

A: General form of quadratic equation:ax2+bx+c=0Quadratic Formula:x=-b±b2-4ac2ab2-4ac=0    one real…

Q: You are given a quadratic equation of the form (x – p)(x – q) = 0. Show that the axis of symmetry of…

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Q: Find the roots of the given Quadratic Equations. 1. x2 - 12 = 0 2. x2 - 16 = 0 3. (x + 3)2 - 20 = 0

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Q: For the following quadratic equation, find the discriminant. 3x2 + 30x + 75 = 0

A: Given :- 3x2+30x+75=0  To find:- Discriminant of given Quadratic equation

Q: Find the  roots of the following equation x^2-2x=10

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Q: Which of the following quadratic equations will obtain 2 rational roots? A. 2x2 +11x + 12 = 0 B. 4x2…

A: To find which of the following quadratic equations will obtain 2 rational roots

Q: Find a quadratic equation whose product of roots x, and x₂ is X₁ X₂ equal to 4 and satisfying the…

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Q: Find the discriminant of the following quadratic equation, and state the number of real roots that…

A: Discriminant The discriminant of the quadratic equation ax2+bx+c=0 is…

Q: 1. Solve the following equations and list all the roots. a) (x² – 25)(x² + 5x – 14) = 0 b) (2x +…

A: Simplify the equation then find roots.

Q: For the following quadratic equation, find the discriminant. 2 x + 15x + 141 = -5x-7 %3D

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Q: Determine the roots of the following quadratic equation, leaving the answer in exact roots. Use the…

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Q: Solve the roots of the equation f(x)=-0.5x^2+2.5x+4.5 a.With the Graphical Method b.Using…

A: Here, we need to find the roots of the equation f(x)=-0.5x2+2.5x+4.5. For (a), Graphical Method:…

Q: Place the following equation into quadratic form. -8 = 2 (x + 9)² O 0 = 2x2 – 36x + 170 O 0 = 2x² +…

A: The given equation is -8=2(x+9)2

Q: Modify the following equation so that it is in quadratic form Determine the values for a, b, and c.

A: In question given question we have to modify the equation in the quadratic form s.t ax2+bx+c=0 and…

Q: Find the quadratic equation given two roots using x^2 - (r + s)x + (r ⋅ s) = 0 1. 3 and 7 2. 4 and…

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Q: If a and b are roots of x2 - 4x - 21 = 0, where a > b, find the equation whose roots are a/b and…

A: First obtain the roots of the given equation as follows.

Q: Solve the following quadratic equations using any method.

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Q: Find the roots, if any, of each of the following quadratic equations by the quadratic formula. 1.…

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Q: Solve the following quadratic equation by using the quadratic formula. If necessary, round to the…

A: Formula:ax2+bx+c=0Roots:x=-b±b2-4ac2aGiven equation:-x2-4x+2=0a=-1, b=-4,…

Q: For the following quadratic equation, find the discriminant. -2x + 36x – 160 = 0

A: -2x2+36x-160=0x2-18x+80=0

Q: If the sum of the roots of the equation 1/(x + a) + 1/(x + b) 1/c is zero, then prove that the…

A: Given that if the sum of the roots of the equation                   1x+a+1x+b=1c, is zero. To prove…

Q: 9.) 9x² + 49 =D0 b.) 2x²-64=0 c) x²-16=0

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Q: Show that the following equation 2x5 – x + 4 = 8* has a solution on the interval (0, 1).

A: we have to show the following equation has a solution on (0,1) . For this we can use intermediate…

Q: 1) 3D1 x 一3

A: Hello! Thank you for your question. We’ll answer the first question since the exact one wasn’t…

Q: Identify the "b" value of the following quadratic equation given below. 6 = (x- 1)2 O 5 O 1 O -5 -2

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Q: Find the formula, in standard form y = ax + bx + c, for a quadratic that has roots at x = 9 and x =…

A: Given that: Roots of the quadratic equation is x=9 and x=-2 & leading coefficient is 1.

Q: Find the roots for each of the following using the quadratic formula. Also, describe the number and…

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Q: OShow that every cubic equation of the form x³ + bx2 + c = 0 where b and c are real numbers has at…

A: Given: x3+bx2+c=0, where b and c are real numbers. The objective is to show that every cubic…

Q: Obtain the roots of the following equation by the fixed point method starting at x = 1 and solving…

A: To obtain the root of 4x2-2x-9=0 using fixed point method with x0=1

Q: For the following quadratic equation, determine the nature of the roots. -5x +10x + 225 = 0

A: Given quadratic equation  -5x^2+20x+225=0 Now we will find the roots and then find the nature of…

Q: the sum of the roots of the equation 1/(x + a) + 1/(x == 1/c is zero, then prove that the product of…

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Q: Place the following equation into quadratic form. -6 = -3(x + 10)2 %3D O 0 = -3x2 – 294 O 0 = -3x –…

A: A quadratic equation is a equation of the form  ax2+bx+c=0

Q: Find ALL the roots of the equation. 1 y = x° + 6x2 + x + 6

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which of the following quadratics has imaginary roots? (1) x² +3x – 5 = 0 (3) 2x² – 3x+1=0 (2) x²…

A: For a quadratic equation: ax2+bx+c=0, the discriminant is calculated using the formula: D=b2-4ac.…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.