Question

If 1/2 is a root of the equation x2 + kx – 5/4 = 0, then the value of k is
(A) 2 (B) – 2 (C) 1/4 (D) 1/2

NCERT Class X
Mathematics - Exemplar Problems

Chapter _QUADRATIC EQUATIONS

Answer 1

Given , 1/2 is a solution of the equation

$( \frac{1}{2} )^{2} + k/2 - 5/4 =0$]
or, 1/4 - 5/4 = -k/2
or, -k/2 = -1
or k = 2

Answer 2

The value of K is 2.1

To find the value of K the first thing to be done is to observe the quadratic equation given and then substitute the value of the X and equate it to zero then the value of K will be found.

Let z be the root of the equation F(X), then F(Z) = 0. Similarly, when we substitute $\frac{1}{2}$ in the given equation $X^{2}+K X-\frac{s}{4}=0$ which results the value should be zero.

$\Rightarrow\left(\frac{1}{2}\right)^{2}+K\left(\frac{1}{2}\right)-\frac{5}{4}=0$

$\Rightarrow \frac{1}{4}+\frac{K}{2}-\frac{5}{4}=0$

$\Rightarrow 1+2 K-5=0$

$\Rightarrow K=2.1$