Question

The graphs of $y=2x^2$ and $y=ax+b$ intersect at two points (2,8) and (6,72). Find the quadratic equation in x whose roots are a+2 and $\frac{b}{4}-1$.

Answer 1

At (2,8) and (6,72), $y=2x^2=ax+b$

$8=2a+b$ and $72=6a+b$.

Solving these equations,

$a=16$ and $b=-24$

The required equation is that whose roots are 18 and -7.

Sum of its root = 11

Product of its root = -126

Therefore, required equation is $x^2-11x-126=0$.