Explain in in words how to solve the 2 question 1) If a third-degree polynomial has a lone x-intercept at x = a, discuss what this implies about the linear and quadratic factors of that polynomial.     2) Describe verbally how to solve. When assumptions have you made about the value of m?

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: Use the given information about the polynomial graph to write the equation. Degree 5. Roots of…

A: In this question, we need to find the polynomial equation using the information given about…

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: Answer the following justifying your answers with examples or by stating theorem(s) used: a) Is it…

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Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

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Q: How many inflection points can a: (a) quadratic polynomial have? (b) cubic polynomial have? (c)…

A: fx be a qudratic polynomial .⇒f''x=constant xtherefore a quadratic polynomial never has any…

Q: verbally   If a third-degree polynomial has a lone x-intercept at x = a, discuss what this implies…

A: Given query is to provide information regarding factor of a 3 degree polynomial.

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: 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: Find the quadratic polynomial if the zeroes of it are 2 and 1/3 respectively.

A: Find the quadratic polynomial

Q: The quotient rule for square roots states that if a and be are nonnegative and b doesn't equal…

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Q: 2. Prove: If ax? + bx + c factors nicely (i.e. the roots are fractions without square roots…

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Q: 1. One of the roots of -5x²(x³ + 2x - 7) is 0. How many other roots are there? А. 3 В. 4 С. 5 D. 6

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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: How many roots are there for the polynomial that factors into f(x) = (x² – 1)(x + 2)(æ – 1)2? 3.

A: no of roots = ?

Q: Given that 1 is a double root of q (x)=D4x4-15x3+16x2_ 3x-2, find all roots. All the roots of q (x)…

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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: Find the zeros of f(x) = x² Enter your values separated by a semicolon. Do not include x = in your…

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Q: 5 Calculate the roots of the following polynomial equations: (a) x³ – 6x² + 11x – 6 = 0 given x = 1…

A: Topic = Polynomials

Q: From the given information find the remainig roots of the polynomial. E(x)=x+4x³+2x²+20x-15, and one…

A: The objective is to find the remaining roots of the given polynomial

Q: Determine the maximum number of real roots and possible real roots of the following polynomial…

A: We know that, a polynomial equation of degree n has maximum n roots.  If a+ib is a root of a…

Q: 5 – 4 Given P(x) and that 3i is a zero, write P in factored form (as a 3x x* + 19x* 13x? — 72х — 36,…

A: A function of the form p(x)=anxn+an-1xn-1+⋯+a1x+a0, where, an≠0, a1,a2,...,an∈ℝ and n∈ℕ∪0 is said to…

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: Find the roots of the functionf(x) = (2x−1)·(x2+ 2x−3) withx∈R

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Q: If -5 is a rooot of the quadratic equation 2x2+px-15=0 and the quadratic equation p(x2+x)+k=0 has…

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Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: 5 (a) Compute the roots of the quadratic polynomial s² + 2s + 5. (b) Is the polynomial s2 + 2s +5 an…

A: Using square root method we will solve this problem

Q: 12:44 ll 11) What is the quadratic polynomial in standard form Given x = 2,3,-4 Change roots into…

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Q: 2. Which polynomial equation has 1, -2, and 3 as roots? A. P(x) = (x + 1) (x – 2) (x + 3) B. P(x) =…

A: Here in the given question we are provided with roots as 1, -2 and 3. And we are asked to find…

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: Produce the quadratic polynomial interpolating the data {(-2, –15), (–1, –8), (0, –3)}. Find the…

A: We will find out the required equation of quadratic polynomial.

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: Find the roots of the polynomial: f (x) = 2(x – 5)³ + 16.

A: Given f(x)=2x-53+16

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: What are the roots of the polynomial y = x³ – 8? O r = 2, a = -1±iv? O ¤ = 2, x = ±1 O ¤ = 2, x = ±i…

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Q: Use the quadratic formula to show that tthe finction flu=ax2=3A+7 does not produce on cutput of…

A: f(x) = 2x2 -3x +7

Q: 4) -3, -4, 5 ansurer -2 -3 3 answer 6) - answer .

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Q: 2. Apply the Midline Theorem in finding the value of x. Show your solution .B (83x) m

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find a polynomialf (x) of degree 3 that has the following zeros. 6 (multiplicity 2), –1 Leave your…

A: Given; 6(multiplicity 2),-1.

Q: The maximum value of the quadratic form 4x2 – 8xy + 5y² is Select one: 9+65 2 9-V65 2 9 + V65 9+V185…

A: The given expression is u =4x2-8xy+5y2 calculate partial derivatives ∂u∂x=8x-8y=0⇒x=y…

Q: 8. (a) Compute the roots of the quadratic polynomial s² + 2s + 5. (b) Is the polynomial s2 + 2s +5…

A: Given quadratic polynomials2+2s+5a.Discriminant,D=b2-4acD=22-4×1×5D=-16D<0so, this quadratic…

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: Is there a real number ______ whose square is -1? b. Does there exist _____ such that x 2 = −1?

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Q: What is rhe third root of unity ?

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

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

A: .

Q: Choose the letter of the best answer. Write the chosen letter on a separate sheet of рaper. 1. What…

A: Consider the given equation 3x2+5x=6. The general form of a quadratic equation is ax2+bx+c=0, a≠0.…

Q: Calculate the roots of the following polynomial equations: (a) x – 6x2 + 1lx – 6 = 0 given x = 1 is…

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Q: 17. How can you quickly determine the number of roots a polynomial will have by looking at the…

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