Question

find the values of p and q if a^2-1 is a factor of pa^4-7a^3+9a^2+qa-10

Answer 1

Given

$= > p {a}^{4} - 7 {a}^{3} + 9 {a}^{2} + qa - 10 = 0$
a²-1 is a factor of given polynomial

=> a²-1 = 0

=> a² = 1

=> a = ±1
_____________

So

$= > f(1) = 0 \\ \\ = > p {(1)}^{4} - 7 {(1)}^{3} + 9 {(1)}^{2} - q(1) - 10 = 0 \\ \\ = > p - 7 + 9 - q - 10 = 0 \\ \\ = > p - q = 8 \: \: \: ....(eq _{1})$
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$= > f( - 1) = 0 \\ \\ = > p {( - 1)}^{4} - 7 {( - 1)}^{3} + 9 {( - 1)}^{2} - q( - 1) - 10 = 0 \\ \\ = > p + 7 + 9 + q - 10 = 0 \\ \\ = > p + q = - 6 \: \: \: ..(eq _{2})$
______________________

BY [Eq(1)+Eq(2)] we get :-

=> 2p = 2

=> p = 1 _____[ANSWER]
-________

By Eq(2)

=> 1 + q = -6

=> q = -7 ____[ANSWER]

_____________

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_-_-_-_☆$BE \: \: \: \: BRAINLY$☆_-_-_-_

Answer 2

• then by equation 2-

we get 1+q=-6

q=-7.

solved....

hope it will help you....

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