Determine the roots algebraically by fact a) x- 8x2- 3x + 90 = 0 b) x + 9x + 21x - x - 30 = 0 c) 2x-5x – 4x + 3 = 0 %3D

Q: The polynomial + ax 3x+ hx 2 has roots -1 and 2. one of which is a triple root. Find the values of a…

A: There are two possible case, checking one by one both to know which is the possible case as in next…

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: Find the root of 4x³ +3x² + 2x +11 over the interval [-2,–1].

A: We will find out the required root.

Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

A:

Q: (1,6) and perpendicular to 2x+7y=1

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Q: What does Descartes’ Rule of Signs tell you about the real roots of x3 – x2 + 1 = 0 ?

A:

Q: 7.4x+4x3-2Sx2 -x+ 6 0 XI =-3

A: Since you have asked multiple questions, as per company guidelines we will solve the first question…

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: 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: 4. Form the equation whose roots are the multiplicative inverses of the roots of 3x2 + 10x – 8 = 0.

A:

Q: What are the rational roots of 15x3 – 32x2 + 3x + 2 = 0 ?

A: To find: The rational roots of the equation 15x3-32x2+3x+2=0. Given: The equation is…

Q: -) What is the nature of the roots for y 2x - 5? Use the disc to determine the nature of the roots.

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Q: how did you find the root zeros

A:

Q: 6. %3D Determine the number and type of roots of g² + 10 = 3x -3.

A: GIven :  x2 + 10 = 3x -3

Q: The polynomial x^5+x+7=0 has exactly one real root and how would I explain that this root must be…

A:

Q: )) What is the quadratic polynomial in standard form Given x = and -2 1 %3D Change roots into…

A: Please refer to the image below

Q: (a) Factor: x2-2x- 3 (b) What the roots of x2 - 2x - 3 = 0?

A:

Q: A polynomial is given below. 3x° + 2x – x +7 | Which statement must be true about this polynomial?…

A: The degree of the polynomial is 6.  For a polynomial the maximum number of roots are equal to the…

Q: 1-9, FIND THE DEI 1. y = 5x4 – 9x³ + 7x %3D -

A: The solution is :

Q: 4) a) Show that the equation y = x³ + 3x2 + 16 has exactly one real root. What is it

A: To show That the equation y=x^3+3x^2+16 has exactly one real root.

Q: What is the nature of the roots of 3y"+15y+33? What is the nature of the roots of 4y"-12y+16?

A: Nature of the roots of the differential equation

Q: What are all the roots of x5 – x4 – 3x3 + 3x2 – 4x + 4 = 0

A:

Q: show that the equation x^5+2x^3+3x-4=0 has exactly one root. Justify your answer.

A: Given equation has only one root. Here is its explanation.

Q: #7 using Descartes's rule of sign

A: Part (a) The polynomial f(x) = x3 +3x +7 has a degree 3, so, it has 3 roots. For positive real…

Q: ethod of undetermined coefficients to so y" +4y = 2x +2.

A: Given: y''+4y=2x+2

Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: Show the work steps for finding the roots of x- 13x+36 algebraically.

A:

Q: Develop a C program that computes the different roots in a quadratic equation, ax + bX²=0. r = -b ±…

A: we need to compile a C program in order to find the roots of a quadratic equation

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: - (b) Without extracting the roots, determine which one is greater, VII-5 or, 19 – /13.

A: Solution

Q: Show that the equation 6x4 – 7x +1 = 0 does not have more than two distinct real roots.

A:

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

A:

Q: b) Find all the roots of x3+7x²+7x+1%3D0

A: First find the one root by hit and trial method then using long division form the quadratic and…

Q: 7.) What is the nature of the roots for y = 2x – 5? Use the discriminant to determine the nature of…

A: Given:- y = 2x2-5 To find :- Use discriminant determine the nature of roots

Q: Determine the real roots of the equation using open methods (Error≈0.001): f(x) = - 24 + 80x - 90x2…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. The derivative…

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: Show that the equation r1 + x³ + 4x – 2 = 0 has exactly one real root.

A:

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: Show that the equation 5x* = 7x+5 has at most two real roots. %3D

A: To show that the equation 5x4=7x+5 has at most two real roots

Q: What is rhe third root of unity ?

A: This question can be solved using the concept of complex numbers.

Q: What are all the possible rational roots of 2x^3 + 3x^2 - 10x + 4 = 0?

A: Given: - The equation is, 2x3+3x2-10x+4=0 To find: - The rational roots of the given equation.

Q: Prove that the equations 3x+9 = 6 and x+3=2 equivalent. Explain why or why not.

A: Equations that have same roots are called equivalent.

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: Show the work steps for finding the roots of x* – 13x² + 36 algebraically.

A:

Q: • What is the nature of the roots of 3y"+15y+33? What is the nature of the roots of 4y"-12y+16?

A:

Q: what is the roots of x2 _ 5x _ 2 =0 ?

A:

Q: Show that the equation x3 –- 15x + c = 0 has at most one real root in the interval [-2, 2]. |

A:

Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)…

Q: 2. Isabel believes that f(x) = x3 - 9x2 + 27x - 27 has 3 complex roots. Nicky told her that it has 4…

A: Here we will use some basic results.

Q: find the roots x^4-4x^3+8x^2-8x+4=0

A: To find the roots.x4-4x3+8x2-8x+4=0