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C) Find p and q such that 3 and - 1 are the zerosof f(x) = x4 + px3 + qx2 + 12x - 9. |
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Answer» <P>Answer: mark me as the brainliest Step-by-step explanation: we have to find the values of p and q such that 3 and - 1 are zeroes of f(x) = x⁴ + px³ + qx² + 12X - 9 Solution : we know, if x = a is a zero of polynomial, f(x) then f(a) must be equal to zero. i.e., f(a) = 0. similarly, 3 and -1 are zeroes of f(x). so, f(3) = 0 ⇒ 3⁴ + p(3)³ + q(3)² + 12(3) - 9 = 0 ⇒81 + 27p + 9q + 36 - 9 = 0 ⇒27p + 9q + 108 = 0 ⇒3p + q + 12 = 0 ⇒3p + q = - 12.........(1) again, f(-1) = 0 ⇒(-1)⁴ + p(-1)³ + q(-1)² + 12(-1) - 9 = 0 ⇒1 - p + q - 12 - 9 = 0 ⇒-p + q - 20 = 0 ⇒-p + q = 20 ..........(2) from equations (1) and (2) we GET, p = -8, q = 12 |
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