Find p and q such that 3 and -1 are the zeros
of f(x) = x4 + px3 + qx2 + 12x – 9.
Answers
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
Therefore the values of p and q are -8 and -12 respectively.
also read similar questions : Find the values of p and q so that x+1 and x-1 are the factors of x4 + px3 + 2x2 - 3x + q
https://brainly.in/question/5353612
find the value of p if (x-p) is the factor of the polynomial xpower6 -px5+x4-px3+3x-p+2
https://brainly.in/question/1247738