Question

If the roots of the quadratic $2x^2+kx+2=0$ are equal then the value of ${}^{\prime }{k}^{\prime }$ is

• A. $4$
• B. $-4$
• C. $\pm 4$
• D. $\pm 16$

Answer 1

The correct option is C $\pm 4$

Consider the given equations.

$2x^2+kx+2=0$ ……. (1)

Since, the both roots are equals.

Then,

$\alpha +\alpha =\frac{-k}{2}$

$2\alpha =\frac{-k}{2}$

$\alpha =\frac{-k}{4}$

$\alpha \cdot \alpha =\frac{2}{2}$

${\alpha }^2=1$

Therefore,

${\left(\frac{-k}{4}\right)}^2=1$

$\frac{k^2}{16}=1$

$k^2=16$

$k=\pm 4$

Hence, this is the answer.