Question

if one root of 2x 2 +kx+1=0 is -1/2 the value of k

Answer 1

Just substitute the root in the equation, you have 2(-1/2)²+k(-1/2)+1=0 ⇒ k=3

Answer 2

QUESTION:

The correct question should be:

If one root of $2x^{2} +kx+1=0$ is $-\frac{1}{2}$ then, the value of k is ____.

ANSWER:

For the given equation, the value of k is 3.

Given,

Quadratic equation:

$2x^{2} +kx+1=0$

To find,

The value of k, when $-\frac{1}{2}$ is one root of the equation.

Solution,

Here, the given quadratic equation is,

$2x^{2} +kx+1=0$

Now, it is given that $-\frac{1}{2}$ is one root of the equation.

As we know, the roots of a quadratic equation always satisfy the equation.

So, substituting $-\frac{1}{2}$ in the given equation (1), should satisfy the equation.

$\implies 2(-\frac{1}{2}) ^{2} +k(-\frac{1}{2} )+1=0$

$\implies 2(\frac{1}{4}) -(\frac{k}{2} )+1=0$

$\implies \frac{1}{2} -\frac{k}{2} +1=0$

$\implies 1-k +2=0$

$\implies -k +3=0$

$\implies k =3$

Therefore, for the given equation, the value of k is 3.