Question

if 2 and -1 are the two remainders if x-1 and x+2 divides the polynomial ax+xsquare+b, finda and b?​

Answer 1

sorry friend I not help you sorry

Answer 2

SOLUTION

GIVEN

2 and - 1 are the two remainders if x - 1 and x + 2 divides the polynomial ax + x² + b

TO DETERMINE

The value of a and b

EVALUATION

Let p(x) be the given polynomial

Then p(x) = ax + x² + b

⇒ p(x) = x² + ax + b

Now zero of the polynomial x - 1 is 1

Again zero of the polynomial x + 2 is - 2

So by the Remainder Theorem the required Remainder when p(x) is divided by x - 1 is

p(1) = 1 + a + b

Again by the Remainder Theorem the required Remainder when p(x) is divided by x + 2 is

p(2) = 4 - 2a + b

So by the given condition

1 + a + b = 2

⇒ a + b = 1 - - - - - (1)

4 - 2a + b = - 1

⇒ - 2a + b = - 5 - - - - - (2)

Solving Equation 1 and Equation 2 we get

a = 2 & b = - 1

FINAL ANSWER

Hence the required values a = 2 & b = - 1

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