Check the definiteness of the following quadratic form; Q(x1, X2, X3) = 2xỉ + 3x – x + 5x,x3 + X2X3

Q: Which of the following is not a quadratic equation: O(x - 2)² + 1 = 2x - 3 O x(x + 1) +8= (x +…

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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: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A: For solving a polynomial equation put

Q: 29. Select the quadratic polynomial with roots -1 and 4. 22 + 3x – 4 O a3 – 2a? – 7æ – 4 O 4x2 + 8x…

A: It is given that the equation is in quadratic And the two roots of the equations are -1 , 4    This…

Q: Show that the roots of px2 + (p - q)x - q = 0 are real for all real values of p and q.

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Q: Solve the following quadratic equati ons by factorization x+3 1-x 17 (ii) X-2

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Q: O Determine k such kr' -4x+ 0 that has real and different solutions.

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

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Q: Which quadratic has zeroes of 5 and 5/2  A) (q + 5)(5q + 2) B) (q - 5)(2q - 5) C) (q - 5)(5q - 2)…

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Q: Solve the following quadratic equation listed below. 5x2 = 4x2 - 4x - 4 %3D O x= 2, -3 O x = -2 O x=…

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Q: Given that α and β are the roots of the quadratic equation ax2 + bx + c = 0. Show that αβb2 = ac(α…

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Q: Expand (x + 4)(x – 5) and use this answer to write down the quadratic equation in the form ax2 + bx…

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Q: Does the Intermediate Value Theorem guarantee that the following equation has a real solution…

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Q: The quadratic form Q(x) = 3x,² + 7x22 + 4x3? is (a) Positive definite (b) Indefinite (c) Negative…

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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: 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: 14. The condition for the quadratic cquation x2 + 2kx + (k + 6) = 0 to have two uncqual real roots…

A: When a quadratic equation have two real unequal real roots then the value of discriminate is greater…

Q: Solve the following quadratic for all values of x in simplest a+bi form. x +18x+38 = 4x – 20

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Q: 1.Solve the following polynomial equations.  a)  2X2+1=x2+2X

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Q: If w and af are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + w)] + [1/(c + w)] = 2w²…

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Q: Which of the following representations of a quadratic has complex roots? Oal 9x2 + 33 = 0 b) -2.5 -2…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only three subparts…

Q: Answer the following: 1. Characterize the roots of the following quadratic equations using the…

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Q: Which of the following are the factors of the quadratic below? x2 - 5x - 14 O (x-7)(x+2) O x = 7 and…

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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: Which of the following expressions below shows the complete factorization of the quadratic…

A: Break middle term in such a way that it's product should be equal to product of first and last term

Q: find the value of k for which the quadratic equation (k+4)x2+(k+1)X+1=0 has equal roots

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Q: 1. Solve the following quadratic equations by factoring. doidw g. (x+1)(x + 3) = -1 h. x(x + 2) =…

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Q: Decide whether the following statements true or false. Justify your answer. (a) For any real x and…

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Q: Solve the quadratic for x: f (x) = (3x – 6) (4x + 12) Ox= 6 and x = -12 Ox = -2 añd x = 3 Ox = 2 and…

A: We have to solve the quadratic equation: fx=3x-64x+12 To solve the given equation we need to put…

Q: Which of the following mathematical equations could be transformed to quadratic form? * 6. x = 0 1 y…

A: We will find out the required solution.

Q: -termined coefficients were used. No need to actually compute the parti ne constants by plugging in.…

A: Given                                  x''-2x'+x=t2et

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

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Q: The solutions of the quadratic equation x(4x – 3) + 3 = 0 are - O None of these O 3±iv57 8. O…

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Q: Prove that if one root of ax? + bx + c = 0 is twice the other then 2b = 9ac

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Q: Suppose a quadratic equation is given as follows: (k – 1)x² + x + 1 = 0 Select all values of k for…

A: k-1x2+x+1=0 The Formula for discriminant is- D=-b±b2-4ac2a

Q: Decide whether the following statements true or false. Justify your answer. (a) For any real x and +…

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Q: Prove that the equation a3 – 4.x + 2 = 0 has three irrational solutions. Hin %3D but just show that…

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Q: Decide whether the following statements true or false. Justify your answer. (a) For any real x and…

A: We have to conclude that the given statements are true or false?

Q: 4. Find the roots of the following over C (a) x2 + 18x + 97 (b) x3 +3x2 - 6x -8 yes that is a cubic…

A: a)  x2+18x+97 Using the formula, x=-b±b2-4ac2a x=-18±324-3882x=-18±-642x=-18±i82x=-9±4i   c)…

Q: Which of the following are the (solutions) of the quadratic belo x2 -9x +8 O(x-1)(x-8) O (x+1)(x+9)…

A: We have to find the root of the quadratic equations

Q: Place the following equation into quadratic form. 10 = -(x + 7)2 %3D O 0 = -x + 14x - 59 O 0 = -x² –…

A: The given equation is                                       10=-(x+7)2 A quadratic equation is of…

Q: Find all the real roots of the following polynomial equation: 1) (3x + 2) (x² - 25) = 0 2) 2x³ – 3x²…

A: Find the real roots of polynomial equations. According to our guidelines , we can answer only first…

Q: What is the complete factorization of 12r° - 3x²? H. = = = BI U S x, x² | E X2 x?

A: Answer

Q: 9. Which of the following equations matches standard form of a quadratic ax + by = c y = a(x-h)² + k…

A: option B: y = a(x-h)2 + k The above equation is of parabola in vertex form.  Expanding the same will…

Q: Prove that 2r +1 is not a factor of 4r +r - 1.

A: We have to prove that  2x+1 is not a factor of  4x3+x-1.

Q: If w and a² are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + a)] + [1/(c + a)] = 2w²…

A: We have given that, ω and ω2 are the nonreal cube roots of unity. Also, 1a+ω+1b+ω+1c+ω=2ω2…

Q: (i) q(x) = 3x2 + 2xy +5yz + 7y2 – 2z2 %3D -

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Q: Find the value(s) of k so that the quadratic equation x2 + kx + 2x + 4 = 0 has one real, distinct…

A: Explanation and solutions is given below.....