1. P(x) = px' –8x² +qx +2 is divisible by 2x-1 and when divided by x-1, the remainder is 3, where p and q are constants. a. Find the values of p and q. b. Hence, using long division, factorize P(x) completely. c. Find all roots of P(x) if P(x)=0.

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

A:

Q: Let P(x) = x* - 4x + 4x + 16x² - 17. Write the terms of P(x) in descending powers of x and use…

A:

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

Q: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

A:

Q: Given h(r)=−r6+12r^5−80r^4+492r^3−1611r^2+2160r−972 and 6i is a zero of h, answer the following…

A: As many parts are given , I will solve only the first 3 parts : We are given :…

Q: Consider the polynomial p(x) = 2æ³ + 5æ² 18x + 9 which has rational root x = 3/2. %3D Find the two…

A: x=a is said to be a root of a polynomial f(x)=0 iff (x-a) is a factor of f(x).

Q: If x = -1 is a root of the polynomial 0 = x3 + 4x? + 2x – 1, what are the remaining roots? -3+V13 x…

A:

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

A: Topic = Polynomials

Q: Use synthetic division to solve: Show your work for credit. x' - 4x* – 2x' + 4x? +x = 0 Hint: This…

A:

Q: f(x) = x + 9x² + 8x – 60 %3D

A: detailed solution is given below

Q: 5) Use long division to find the quotient Q(x) and remainder R(x). P(x) = 6x³ 2x² + 4x - 1 and d(x)…

A:

Q: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

A:

Q: Suppose Q is a polynomial of degree n>= 2 with distinct roots, none lying on the real axis.…

A:

Q: 1/2x2 + x − y − 2 = 0 Find the zeros if any

A:

Q: 3. Divide f(x)= x³ + 2x² - 2x+4 By (x-2) using synthetic division. What is the remainder?

A:

Q: Given that x = 2 is one root of g(x) = 2x* + 4x – 9x² – 11x – 6 = 0, use factorisation to determine…

A:

Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: For each polynomial the corresponding number k is a root of f(x). Use synthetic division to factor…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…