6 of 12 9.3b | Use the discriminant to predict the number of solutions of a quadratic equation Use the discriminant to predict the number of real solutions:

Q: 1. Which of the following is a quadratic equation? [NCERT Exem (a) x2 + 2x + 1 = (4-x) + 3 (b)- 2x…

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Q: Use the proof by cases to prove that there are no solutions in integers x and y to the equation 4x?…

A: Here we use the fact that x2≥0 and y2≥0 and will be square of some integers. So possible values of…

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: Prove the following equations

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use the Intermediate Value Theorem in Exercise to prove thateach equation has a solution. Then use a…

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Q: The set of solutions to z =-V2 - V26 is

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Q: Use the quadratic formula to solve for x. 2x-2x-1=0 (If there is more than one solution, separate…

A: The general quadratic equation is of the form ax2+bx+c=0, where a, b and c are the coefficients. The…

Q: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: Find the vlaue of k for which the quadratic equation (k+4)x2+(k+1)x+1=0 has equal roots

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Q: It is given that a and B are the roots of the quadratic equation 2x+4x- 3 = 0. Form a quadratic…

A: If α and β are the roots of the quadratic equation ax2+bx+c=0, then α+β=-baαβ=ca Consider the…

Q: 16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

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

Q: Let B be a random number chosen from the interval (-10, 10). Find the probability that the quadratic…

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Q: 11. Without solving, determine the number of real solutions for each quadratic equation. Show work.…

A: Given:- a) 5q²-3q-6=0 b) 3y²-5y +9=0  To find:- Number of real roots of given quadratic equations

Q: Show that the solution (if exists) is unique:

A: Given, u =6x + 4y +2 on {x² + 4y² <1} u(x, y) = x+2y+y²-4xy²-8y³ on {²+4y²=1} Using maximum…

Q: If a, b, c are integer powers of 2, prove that equation a + 64 = does not have solution, otherwise…

A: Given: Let a,b,c are integer powers of 2 .

Q: 4. The roots or solutions of x² + x + 1 = 0 are nonreal. %3D

A: We are solving the first question and for the next question post the question again and also mention…

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

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Q: 4 Get all the roots of 2(V3i – 1) |

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Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

Q: Find the equation of a quadratic function that has the following root x = 5i and x = - 5i and passes…

A: We need to find the equation of a quadratic function that has the following root x = 5i and x = - 5i…

Q: Solve the equation Doe the Ivr consisting of the equation in purt@ and the Condition ylo)31 have…

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Q: Solve the Fol| owing linear ryctems completely and nece ssary solutions. Computations. show all 3x 2…

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Q: Prove that zero is a root for the equation ax' + bx² +cx+d = 0 if and only if d = 0. What can you…

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Q: Show that the equation  x4 + 4x + c =0 has at most tworeal roots.

A: Given: The method of contradiction is used to prove that the above equation has at most  two roots.

Q: 6. Determine the four roots of the equation (z–2)*+(z+1)' = 0 and plot them on an Argand diagram.

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Q: (a) If Q: R"R is a quadratic form, ex that O takes on

A: Given, Q : ℝn→ℝ is a quadratic from,

Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

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Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: Exercise 6: Consider the equation x" + ax + b = 0, with n E N. Show that the equation has at most…

A: First of all consider f(x) as x^n +ax + b.Then we need to differentiate f(x) w.r.t. x and get f…

Q: and such that the sum of their squares is as small as possible. Give the sum of the squares.

A: Given problem:- 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such…

Q: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: (4) Show that in general the sum of the roots of a quadratic equation ax? + bx +e=0 b is --whereas…

A: Let u and v be the roots of a quadratic equation ax2+bx+c=0. To obtain the equation from the roots,…

Q: Refer to the second row Of the toble. 0.06X + 0.1(4600) = 0,09 (x t4500) %3D Solve the eguation 0.06…

A: Given

Q: Find the complete or particular solution of the following diffi- rential equations:

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Q: 1. Use the graph of y = VI to estimate the solution(s) to the following equations YA -150 -120 -90…

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Q: Solve one of the roots of 6x^2 - 5x = 6 - 5i. Express your answer in rectangular form in 4 decimal…

A: We have to use quadratic formula  Roots of  ax2+bx+c=0                x=-b±b2-4ac2a Also we have to…

Q: 23. Use the quadratic formula to find all solutions in the interval 0° ses360° to the nearest tenth…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: %3D 8. Use the Intermediate Value Theorem to prove that the equation e~² + x² = 4 has a real root.

A: Here use the intermediate value theorem and show that the equation e-x + x2 = 4 has a real root.…

Q: Solve for x in x² + 12 < 7x. а. b. Find all possible values of x if one of the interior angles of a…

A: Given query is to find the value of x .

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

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: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: 7.For which value of k will the roots of 2x + kox+1 = 0 be real? .2 1) 1 2) 2 3) 3

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Q: 16, 25-를 = 2P x 59. (a) Find the value of each of the integers p and q for which (b) (i) Express the…

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Q: 3.2 Check the definiteness of the following constrained quadratics: (i) Q(x, y) = x2+ 4xy - y²,…

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--

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.…