Question

please answer with steps

Answer 1

p(x) = 6x³+11x²+kx-20

q(x) = 9x²-5x

Now, let p(x)+q(x) = g(x)

g(x) = (6x³+11x²+kx-20) + (9x²-5x)

= 6x³+11x²+kx-20+9x²-5x

= 6x³+11x²+9x²+kx-5x-20

= 6x³+20x²+(k-5)x-20

g(2) = 6×(2)³+20×(2)²+(k-5)×2-20

= 48+80+2(k-5)-20

= 108+2(k-5)

given, p(2) = 0 [x=2 is the root of g(x)]

108+2(k-5) = 0

2(k-5) = -108

k-5 = -108/2 = -54

k = -54+5 = -49