Question

Let fx=x^3+kx^2+hx+6 find the value of h and k so that x+1 and x-2 are the factors of fx

Answer 1

Solution:-

given 》 fx=x^3+kx^2+hx+6

》factor = x+1 and x-2

》then, let x= -1

》(-1)^3 +k×(-1)^2-2h +6 = 0

》-1 +k-2h+6 = 0

》k-2h = -5.............(1)

》let, x = 2

》(2)^3 + k(2)^2 +2h +6 = 0

》 8 +4k +2h +6 =0

》4k +2h = -10.........(2)

》additing eq(1) and(2)
_______________________

》5k = -15

》(k = -3)

》put k's value in eq(1)

》k-2h = -5.............(1)

-2h = -2

》(h = 1)

》answer (h,k) = (1, -3) ans