Question

If x square -3x +2 is a factor of x power 4 -px square +q. Find the value of p and q

Answer 1

Heya!!!!!
here is your answer...

Answer 2

${\bold{\huge{\mathbb{\orange{Hëy Frïèñd...}}}}}$⭐

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Here is the Solution...

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Let g(x) = x² - 3x + 2

and f(x) = x⁴ - px² + q

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g(x) is a factor of f(x)

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= x² - 3x + 2

= x² - 2x - x + 2

= x(x - 2) - 1(x - 2)

= (x - 2)(x - 1)

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Then (x -2) & (x - 1) is also a factor of f(x)

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1st..

f(2) = 0

So,

f(2) = (2)⁴ - p(2)² + q = 0

= 16 - 4p + q = 0

= 16 = 4p - q (equation 1)

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f(1) = 0

So,

= (1)⁴ - p(1)² + q = 0

= 1 - p + q = 0

= 1 = p - q (equation 2)

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Now, subtracting (equation 2) from (equation 1)

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(Subtraction and further calculation is in the attachment)

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${\bold{\boxed{\huge{\mathcal{Answer..}}}}}$

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${\bold{p = 5 \: and \: q = 4}}$

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I Hope This Will Help You ❣️