Question

If the roots of the equation 2 $x^2$ - 22x + k = 0 are 7 and α, find k ___

Answer 1

First we will find the value of α using the result for sum of the roots.

Once we have α, we will find k using the result for product of the roots.

In the equation a $x^2$ + bx + c = 0,

Sum of the roots = $\frac{-b}{a}$ and product of the roots = $\frac{c}{a}$

7 + α = $\frac{22}{2}$

= 11

$\Rightarrow$ α = 4

So the roots are 7 and 4

Product of roots = $\frac{k}{2}$

Or 28 = $\frac{k}{2}$

$\Rightarrow$ k = 56