Question 27

Explanation

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - bx + 6 = 0$, so we get

Let $p$ and $q$ be the roots of the equation $x^2 - 4x + c = 0$, then

Next, substitute the value $\alpha = 2$ into the first quadratic equation to obtain

So $p = \alpha + \beta = b = 5$, then substitute the value $p = 5$ into the second quadratic equation to obtain

The quadratic equation that has roots $b = 5$ and $c = -5$ is