If the sum of the roots of the equation $x^{2} - x = k (2 x - 1)$ is zero, find $k$ .

Open in App

Solution

$x^{2} - x = 2 k x - k$
$x^{2} - (2 k + 1) x + K = 0$
sum of roots= $2 K + 1 = 0$
$k = \frac{- 1}{2}$

Suggest Corrections

Similar questions

If 3 is root of the quadratic equation $x^{2} - x + k = 0$ , find the value of p so that the roots of the equation $x^{2} + k (2 x + k + 2) + p = 0$ are equal.

Q. Find the value of k for which the equation x²+k(2x+k-1)+2 has real and equal roots.

Q. If 3 is a root of the quadratic equation

x^{2} - x + k = 0

, find the value of p so that the roots of the equation

x^{2} + k (2 x + k + 2) + p = 0

are equal.
[CBSE 2015]

Q. If the sum of the roots of the equation x² − x = λ(2x − 1) is zero, then λ =

(a) −2
(b) 2
(c)

- \frac{1}{2}

(d)

\frac{1}{2}

Q. If the sum of two roots of the equation

x^{3} - 3 x^{2} - 16 x + k = 0

is zero, then

k

is equal to

Join BYJU'S Learning Program

If the sum of the roots of the equation x2−x=k(2x−1) is zero, find k.

x2−x=2kx−kx2−(2k+1)x+K=0sum of roots= 2K+1=0 k=−12

If the sum of the roots of the equation $x^{2} - x = k (2 x - 1)$ is zero, find $k$ .

$x^{2} - x = 2 k x - k$
$x^{2} - (2 k + 1) x + K = 0$
sum of roots= $2 K + 1 = 0$
$k = \frac{- 1}{2}$