Question

Find the value of k such that the sum of the squares of the roots of the quadratic equation $x^2-8x+k=0$ is 40

• A. 12.00
• B. 12
• C. 12.0

Answer 1

Answer: (A), (B), (C)

Let $\alpha ,\beta$ be the roots of the given equation,
Then, sum of roots, $\alpha +\beta =-\frac{-8}{1}=8$
And, product of roots, $\alpha .\beta =\frac{k}{1}=k$

Now, sum of the squares of the roots $=40$

$\Rightarrow {\alpha }^2+{\beta }^2=40$

$\Rightarrow (\alpha +\beta {)}^2-2\alpha \beta =40$

$\Rightarrow (8{)}^2-2k=40$
$\Rightarrow 64-40=2k$
$\Rightarrow 24=2k$
$\Rightarrow k=12$