Question

for which values of a and b , the zeros of q(x)=x^3-2x^2-x+a are also the zeros of polynomial p(x) =x^5-2x^4-10x^3+20x^2+9x+b​

Answer 1

Given :

• q(x) = x³ - 2x² + x + a and p(x) = x⁵ - 2x⁴ - 10x³ + 20x² + 9x + b

To Find :

• The values of a & b.

Let us first divide q(x) with p(x).

Have a look at the attachment!

We got the quotient as x² - 9.

Let us make the remainder = 0.

So,

( 2 - a ) x² + ( b + 9a ) = 0

⟹ 2 - a = 0

⟹ - a = - 2

$\boxed{ \sf{ \red{a = 2}}}$

⟹ b + 9a = 0

⟹ b = - 9a

⟹ b = 9 × 2

$\boxed{ \sf{ \green{ b = - 18}}}$

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Now let's take the Quotient to Find the value of x.

⟹ x² - 9 = 0

⟹ x² = 9

⟹ $\sf{x = \sqrt{9} }$

⟹ $\boxed{\sf{x=3}}$