Given f(x) = 2x ^ 2 + kx - 20 and the remainder when f(x) is divided by x - 10 is 90, then what is the value of k?

k =  -9

Step-by-step explanation:

f(x) = 2x²+kx-20

From remainder theorem,

x = 10 and f(10) = 90

f(10) = 90

Subsitute the value of x into the expression above.

f(10) = 2(10²)+10k-20 = 90

200+10k-20 = 90

Solve for k by collecting like terms

10 k = 90+20-200

10k = 110-200

10k = -90

k = -90/10

k = -9.

Hence the value of the constant is -9