Question

If b^(2) = 4ac, then prove that (ax^(2) + bx + c) is a perfect square.

Answer 1

$\star\:\:\bf\large\underline\blue{Question:-}$

• If b²=4ac, prove that ax²+bx+c is a perfect square.

$\star\:\:\bf\large\underline\blue{Solution:-}$

${b}^{2} = 4ac$

$\implies {b}^{2} - 4ac = 0$

Now, since the discriminant is equal to zero.

Therefore,

ax²+bx+c is a perfect square.

$\star\:\:\bf\large\underline\blue{Hence\:Proved.}$

Answer 2

since, discriminant is equal to zero.

i.e.,

b²-4ac=0, therefore,

ax²+bx+c is a perfect square.