Find $k > 0$ , if the roots of the quadratic equation $x^{2} + k x + 40 = 0$ are in the ratio $2 : 5$

Open in App

Solution

The roots of the equation are in ratio $2 : 5$
Let the roots be $2 a$ and $5 a$
then , sum of roots $= 2 a + 5 a = 7 a = - k$ ...(i)
Product of roots $= (2 a) (5 a) = 10 a^{2} = 40$
$a = \pm 2$
Put the value of $a$ in equation (i)
$7 (\pm 2) = - k$
$k = \pm 14$
Since $k > 0$ , $k = 14$

Suggest Corrections

Similar questions

3 x^{2} - k x + 14 = 0

7 : 6

k

k

x^{2} - k x + 25 = 0

k

2 x^{2} + k x + 3 = 0

For what value of k, the roots of the quadratic equation kx (x - 2 root5 )+ 10 = 0 are equal?

Join BYJU'S Learning Program