If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is

Solution:

Let $\alpha$ and $\beta$ be the roots of quadratic equation $2 x^{2}+k x+4=0$ in such a way that $\alpha=2$

Here, $a=2, b=k$ and,$c=4$

Then , according to question sum of the roots

$\alpha+\beta=\frac{-b}{a}$

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

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

$\beta=\frac{-k-4}{2}$

And the product of the roots

$\alpha \cdot \beta=\frac{c}{a}$

$=\frac{4}{2}$

$=2$

Putting the value of $\beta=\frac{-k-4}{2}$ in above

$2 \times \frac{(-k-4)}{2}=2$

$(-k-4)=2$

$k=-4-2$

$=-6$

Putting the value of $k$ in $\beta=\frac{-k-4}{2}$

$\beta=\frac{-(-6)-4}{2}$

$=\frac{6-4}{2}$

$=\frac{2}{2}$

$\beta=1$

Therefore, value of other root be $\beta=1$

Thus, the correct answer is $(d)$