If a,b,c,d, and e are real numbers and a ≠ 0, then the polynomial equation ax଻ + bxହ + cxଷ + dx + e = 0 has a.Only one real root b. At least one real root c. An odd number of real roots d. No real roots e. No positive real roots

Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: The polynomial f(x)=x^4+6x^3+ax^2-54x+c has four real roots r1, r2, r3, r4 such that r1+r2 = 0 and…

A: The polynomial f(x)=x^4+6x^3+ax^2-54x+c has four real roots r1, r2, r3, r4 such that r1+r2 = 0 and…

Q: To find the roots of a quadratic polynomial ax + bx+C you can use the Quadratic Formula -b+ b2- -…

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Q: (a) Factor f (x) =x'- 3x +4x – 12 into factors of the form (x- c), given that 3 is a zero. (b) Solve…

A: a. Given f(x)=x3-3x2+4x-12 we need to convert in factors and 3 is one of the zero of the equation…

Q: 5) If you know the roots for a polynomial are x = -3, 1, and 2   which of the following could be the…

A: Given: If you know the roots for a polynomial are x = -3, 1, and 2 which of the following could be…

Q: The coefficient of x' in the cubic polynomial g(x) is a, where a >0. The repeated roots of the…

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Q: A polynomial function p(x) has exactly four roots: -2i, 2i, -5, and 1. Which of the following could…

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Q: A polynomial is known to have the following roots x₁ = 4.9+ -4.3 i x2 = 2.3 x3 = (4.6) ¹/2 Determine…

A: If the root is complex number of a real coefficients polynomial then it has complex conjugate root.…

Q: If a,b,c, d, and e are real numbers and a ± 0, then the polynomial equation ax +bx + cx + dx + e = 0…

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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: ind the roots of the polynomial: f(x) = x^4 + 4x^2 – 32

A: Explanation: Given that,  f(x)=x4+4x2-32     Let us suppose  x2=u Function becomes  u2+4u-32

Q: Give an expression for f(x) with leading coefficient –5, of degree 3, and having roots ¤ : -4 , x =…

A: from the given data: i^2= -1 Substituting in the required place and finding the polynomial

Q: Which of the following is a root of the polynomial x? – 4x + 13? O A. 3+ 4i O B. 2 – 3i O C. 4- 5i O…

A: We have to find roots

Q: Find the values of k for which the equation x3+5kx+16=0 has no real roots

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Q: 10. Which of the following is the polynomial equation if the roots are: -1, 0, and 1? A. x3 + x = 0…

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Q: Find a formula for the polynomial P(x) with • degree 3 • real coefficients • zeros at a = -5-2i and…

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Q: 1. If a polynomial function p(x) has real roots of -7, 2, and 3, which of the following must be a…

A: Given that: The given polynomial p(x) has real roots of -7, 2 and 3.

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: Determine the set of values of k for which the equation (3-2k)x + (2k – 3)x+1 = 0 has no real roots.

A: For no real solution of quadratic equation, Discriminant (D) < 0

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x² + ax + ß with…

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Q: (b)If x is so small that its fourth and higher powers may be neglected show that (1 + x) + V(1- x) =…

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Q: X^4 -3x^3 -x^2 -9x -12=0  Find all rational

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Q: Suppose that a polynomial equation has the following six roots: -9, -6, 1 + i/2,1 – i/2, 6, and 9.…

A: Here, the required polynomial has six roots: -9,9,-6,6,1+i2, 1-i2

Q: A Find the complete set of possible rational roots of the following polynomial equations. 154 2.…

A: To complete the set of possible rational roots.

Q: 17. Find all roots of the polynomial P(x) = x* – x³ – x² - x– 2.

A: This question is about nth root of polynomial

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

A: Given  x3 + 2x2 - 5x - 6=0  since one root of the given polynomial is x=1  Therefore (x+1) is a…

Q: Which of the following are the solutions to the polynomial equation x - 13x +36 0? O a. x = 0, 4, 9…

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Q: 2. The roots of a quadratic are x = -5 and x = 3. Which of the following are possible factors of the…

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Q: Find all sixth roots of I, by solving the equation 1. [Hint: Find the zeros of the polynomial f(x) =…

A: Use the following formulae, to obtain the solution. a2-b2=a-ba+ba3-b3=a-ba2+ab+b2a3+b3=a+ba2-ab+b2

Q: A quintic polynomial (degree 5) P(x) has rational coefficients. If -3, v2, and 1+i, are roots of…

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Q: Give an expression for f(x) of degree 3 with roots a =1 , x = 5 + 3i, and a = 5 – 3i. • Your final…

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Q: 1- f(x) = x³ + 2x +1 has 3 roots in Z6- a) True b) False ) a) True

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Q: ). A polynomial equation whose roots are {-1, 1 and 7} is A. x - 7x2 -x-7 =0 B. x + 7x? – x -7=0 C.…

A: Given: To find a polynomial equation whose roots are {-1, 1 and 7}

Q: According to Descartes' Rule of Signs, how many positive real solutions are there to the polynomial…

A: Now we will find the correct option.

Q: What is each term in a polynomial made up of? A O Variables and coefficients. BO Imaginary numbers.…

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Q: If a,b,c, d, and e are real numbers and a ± 0, then the polynomial equation ax +bx + cx° + dx + e =…

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Q: Let p(x)-x-5x?+4x-20. Verify that p(5)-0 and find the other roots of p(x)-D0.

A: p(x)= x3 - 5 x2 + 4x -20   Verify that p(5)=0; p(5)= 53- 5*52+4(5)-20 p(5)=0   Hence, x= 5 is one…

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

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Q: (a) Construct a polynomial x+2x+3x+4 (b) Find out the value of the above for x-1,2,3 (c) Calculate…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: The polynomial x^3-7x+c, where C is a real number, has roots of 1 and -3. Find the third root

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Q: If f'(x) has no roots, then f (x) has exactly one root. If f (x) has three roots, then f'(x) has at…

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Q: Which polynomial expression of fourth degree has the roots x=-3,x%=3,x%= 5i ? A x +16x-225 B…

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Q: 3. Which of the following polynomial equations has 2 as one of the roots? А. X2 — 5х + 8 %3D0 В. 4x3…

A: For the solution follow the next step.

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: Find the value of k in the equation x2 – 3x + k = 0 if its roots are real, irrational and not equal.

A: Since you have multiple questions in a single request. we would be answeringonly the first question…

Q: A quadratic polynomial y = 4x2 +7x – 3 has roots p and q. Find a quadratic g(x) = x² + ax + ß with…

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Q: According to Descartes' Rule of Signs, how many negative real solutions are there to the polynomial…

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Q: (a) Is there any real number c for which qı,-(c+1).c does not have real zeros b) Find a E R for…

A: Given that (a) To find any real number c for which q1,-(c+1),c does not have real zeros: (b) To find…

Q: Find the roots of the polynomial equation. x3- 2x2 + 10x + 136 =0 Select one: O a.-3 + 5 i, -4 O b.…

A: Given,  A polynomial of degree 3 : x3 -2x2 + 10x + 136= 0

Q: 10) If a, b and c are the roots of the polynomialz + 13r- 23 and sum of the roots is 0, then find…

A: The detailed answer is given below Thank you