Question

$16x^2+40x+K$ is a perfect square polynomial, then k =

Answer 1

Given $16x^2+40x+k$ is perfect square for a perfect square

$b^2-4ac=0$

$\Rightarrow (40{)}^2=4\times 16\times k$

$\Rightarrow k=\frac{40\times 40}{4\times 16}$

$\Rightarrow \frac{100}{4}$

$\Rightarrow 25$

$\therefore 16x^2+40x+k$ is a perfect square if $k=25$.