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
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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
⟹ b + 9a = 0
⟹ b = - 9a
⟹ b = 9 × 2
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Now let's take the Quotient to Find the value of x.
⟹ x² - 9 = 0
⟹ x² = 9
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Attachments:
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