Find A+B in the following question:

Question

The vertex of a quadratic polynomial y= 4x^2 - Ax + B will be at (2,0) on the x-axis if the value of A+B=h. Find the value of h where h is a positive integer.

Answer 1

y=4x^2-Ax+B . This quadratic equation strikes at(2,0). Hence x=2 and y=0 will satisfy this equation.

We have, 0=4 X 2^2 - A X 2 +B.

A=(16+B)/2--------------------1

then since the equation strikes on the x-axis we have x=-b/2a

So, x=-(-A)/2 X 4 (but x=2)

Hence A=2 X 4 X 2=16

Now B= 2 X A - 16 = 16

Hence A+B= 16 + 16 =32