If a, b are the roots of x2 + px + 1 = 0 and c, d are the roots а, of x? + qx + 1 = 0, then the value of (a – (C) (b – (C) (a + (D) (b + (D) is (B) q² – p² (A) p² – q? (C) q² + p² (D) none of these

Q: 1. Discuss the possibilities for the roots to : 2x-5x -6x+4 = 0

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Q: if y3-3ax2+x3=0,then prove that y2+ 2a2x2y-5=0

A: Let dy/dx= y1 and d2/dx2=y2 And We will use the product rule of differentiation.

Q: How do I complete the square on thsi following polynomial: x2-6x+12-y=0 To end up with:…

A: x2-6x+12-y=0 cannot be expressed as (x-3)2+4-y=0 because (x-3)2+4-y=0 when expanded will give…

Q: 3. Find the roots of ( x2-1) ( x2 + 3x – 2)=0

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Q: Let (x1, y1) = (7, 2) and (x2, y2) = (1, -1). Find √[(x2 - x1)2 + (y2 -y1)2]. Express the answer in…

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Q: 5x +3x+2=0 has 2 real solutions. O True False

A: We have to determine whether statement is true or false

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: Find the formula, in standard form y=ax2+bx+cy=ax2+bx+c, for a quadratic that has roots at x = -3…

A: We have to find a quadratic that has roots at x = -3 and x = -2, and has leading coefficient of 1.

Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

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Q: Find the general solution to the nonhomogeneous, lincar difference equation X+2 - 4x = 6t - 1 By…

A: Difference equation

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

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Q: 3. Use Graeffe's Root Squaring Method to de the real roots of the polynomial equation х3 + За? — 6х…

A: GRAEFFE'S ROOT SQUARING METHOD:   The roots of any polynomial equation with real coefficients can be…

Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: Given: Z3i=a+bi|a,b∈Z3       =0, 1, 2, i, 1+i, 2+i, 2i, 1+2i, 2+2i We have to find all solutions for…

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: (c) Express the quadratic form Q(x1,42. 43) = 6xj + 3x+3x-4xx2 - 21213 + 4xar1 to the sum of square,…

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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: 15. Given the equation 3x-4x -12 =0, how many roots are there? Rational or irrational?

A: Given equation  3x2-4x-12 = 0 ....... (1) Quadratic formula for the solution of the quadratic…

Q: Use the fact that x'-6x = 2 has no integer solution to prove there do not exist 3 consecutive…

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Q: 5. Find a polynomial equation with real coefficients that has the given zeros: - 3, 4i

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Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

Q: 9. Find the general solutions of X' = AX with A =

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Q: 8. For every quadratic there are two roots (or zeroes or x-intercepts). They are always given by Vb²…

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Q: nswer on 1. Find all the roots of 2x* + x – 8x2 – 4x = 0 | x = -2, x = -0.5, x= 0, x = 2 Bx= -2, x =…

A: Given query is to find the roots of the expression.

Q: Given that f(x) = 12x' - 32x2 + 3x + 5, obtain signs of f(-1), f(0). f(1), f(3) and deduce that…

A: Given that f(x)=12x3-32x2+3x+5 Let us find the signs of f(-1); f(0); f(1); f(3)…

Q: Find the roots of  Z²- 4Z+13 = 0

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Q: 4. Is it possible for a 6th degree polynomial with real coefficients to have 6 imaginary solutions ?…

A: To explain about the polynomial

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5 =0

A: Given : y^3 - 3ax^2 + x^3 = 0

Q: A quartic polynomial P(x) has rational coefficients. If √2 and 1 + i are roots of P(x) = 0, what are…

A: The detailed solution is as follows below:

Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: ! and A quadratic polynomial y = 4x? + 7x – 3 has roots pand q. Find a quadratic g(x) = x2 + ax + B…

A: To find out the quadratic equation.

Q: What are all the possible rational roots of 2r'+3x-10r +4=0? +1, + 2, +4 only +1, ± 2, t 4, only ±늑…

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Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: 42. What is the polynomial equation whose roots are {-2, 2, and 4 of multiplicity 2} A. 2x* - 2x +…

A: As per bartleby guidelines we only give first question answers.

Q: 1. Write the equation to the polynomial with double roots at 3 and 6, that levels off as it passes…

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Q: what is the factored form of ax^2+bx+c where the roots are x1 and x2?

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Q: 19. What is the largest value of the quadratic form 5(x,)? - 3(x2)² if x²x = 1. 20. What is the…

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Q: (2) Determine k such kx² – 4x +- = 0 that has real and different solutions.

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

Q: Find a real root of 3*exp(-x/2)+4*In(x)-2 = 0 using False Position method with a=0.5 and b=2.0…

A: Given:            3*exp(-x/2)+4*ln(x)-2=0           3·e-x2+4lnx-2=0     By using False position…

Q: Mr. Bean has a 5th degree polynomial using only the variable x. Mr. Kelly has a different 5th degree…

A: Mr. Bean has a 5th-degree polynomial using only the variable x. Mr. Kelly has a different 5th-degree…

Q: What are the possible rational roots of the equation x + 6x2 11x + 6 = 0 A. -6, -3, -2, -1 C.+6, +3,…

A: Rational roots of polynomial  Let us consider a polynomial of the form…

Q: Find the value of the constant "k": 3x^2-5x+ 4k-5-0 has one root equal to 0.

A: We will use formula for root of quadratic equation

Q: What are all the possible rational roots of 2x³ + 3x² – 10x +4=0? 글 only A B +1, ±2 only +1, ± 2, ±…

A: Possible ration rational of any polynomial are ±Factors of constant termleading coeficient Therefore…

Q: Find the roots of z3= -2

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Q: If x = -1 is a root of the polynomial 0 = æ³ + 2x2 – 5z – 6. what are the other roots? Ox =-3, x = 2…

A: see next step

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: 3. Let 7, r, and r, be the roots ofx' +3x-5x-4= 0, construct the equation whose roots are: 7(r, +r3…

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Q: Whatis the value of r in the quadratic equation x² – 10x – r = 0 whose roots are equal rational and…

A: .

Q: find the four zeroes of the polynomial z^4+4, one of them being z0=2^1/2e^ipi/4=1+i.then use those…

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Q: Find a real root of 4*exp(-x/2)-3*In(x)-3 = 0 using False Position method with a=0.1 and b=2.0…

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Q: Determine the roots of f (x) =-12-21x + 18r - 2.75x using the false-position method, with initial…

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