Question

If one root of 2x^2+kx+1=0 is -1/2 then what is the value of k? Please explain the answer

Answer 1

Answer:

The value of k is 3.

Step-by-step explanation:

Polynomial($\\ x$) = $\\ 2x^{2} + kx + 1 = 0$

One of the root of Polynomial($\\ x$) is $\frac{-1}{2}$

Find $\\ k$.

SOLUTION:

We know that $\frac{-1}{2}$ is the root or zero of the polynomial.

So we will substitute the value of $\\ x$ by $\frac{-1}{2}$

Therefore the equation  becomes:

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

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

$\\ \frac{1}{2} + 1 = \frac{k}{2}$

$\\ \frac{1}{2} + \frac{2}{2} = \frac{k}{2}$

$\\ \frac{3}{2} = \frac{k}{2}$

Cross multiply

$\\ 2(3) = 2(k)$

$\\ 2k = 6$

$\\ k = \frac{6}{2}$

$\\ k = 3$  

∴ The value of k is 3.