Question

find the values of p and q if (x-2) and (x+3) are factors of p(x)=x^3-px^2-qx-30

Answer 1

Solution:-

given equetion:-

p(x)=x^3-px^2-qx-30

zeroes are = (x-2) and (x+3)

by ,x = 2

(2)^3 -p(2)^2-2q-30=0
8 - 4p -2q-30 =0
4p+2q = -22.........(1)

by, x= -3

(-3)^3 - p(-3)^2-q×(-3)-30 = 0

-27 -9p+3q -30

-3p+q = 19........(2)

muliply by 2 in eq(2) -eq(1)

-6p+2q = 38..........(2)

4p+2q = -22.........(1)
+_-____+______________

-2p = 60

p = -30 ans

put p's value in eq(1)

4(-30) +2q = -22

2q = -22 +120

q = 98

q = 49 ans

(p,q) = (-30, 49) ans