Question

Let P(x) = ax? + bx,q(x)=2x+ mx+n. If
p(1) – 9(1) = 0, p(2)— 9(2)=1 and P(3) – 9(3) = 4 then
p(4)-9(4)=
​

Answer 1

Answer:

Step-by-step explanation:

I’m assuming you made a typo in p(x) and it is ax^2+bx instead of a^2.

As said in the previous answer, assume f(x) as p(x)-q(x) and since both p(x) and q(x) are quadratic polynomials, f(x) will also be a quadratic polynomial in the form of Ax^2 + Bx + C.

f(1) = A + B + C = 0

f(2) = 4A + 2B + C = 1

f(3) = 9A + 3B + C = 4

Solving these three equations, we get A = 1, B = -2 , C = 1

We need f(4) = 16A + 4B + C = 16*1 + 4*(-2) + 1 = 16 - 8 + 1 = 9

Therefore, f(4) will be equal to 9

Hope this helped!