find-k-if-y-2-y-k-is-a-perfect-square-

Question Number 145057 by 7770 last updated on 02/Jul/21

f i n d k i f y^{2} + y + k i s a p e r f e c t

s q u a r e

Commented by mr W last updated on 02/Jul/21

y^{2} + y + \frac{1}{4} = {(y + \frac{1}{2})}^{2}

\Rightarrow k = \frac{1}{4}

Commented by 7770 last updated on 02/Jul/21

s o r r y i t s y^{2} + y + k i s a p e r f e c t s q u a r e

Commented by imjagoll last updated on 02/Jul/21

y^{2} + y + k \to perfect square if △ = 0

\Rightarrow 1 - 4 k = 0; k = \frac{1}{4}