16x^2 + 40x + k is a perfect square polynomia | vedclass

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Question

(D) quadratic expression $ax^2 + bx + c$ is a perfect square if its discriminant $D = b^2 - 4ac$ is equal to $0$.Here,$a = 16$,$b = 40$,and $c = k$.Se

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) quadratic expression $ax^2 + bx + c$ is a perfect square if its discriminant $D = b^2 - 4ac$ is equal to $0$.Here,$a = 16$,$b = 40$,and $c = k$.Setting the discriminant to zero: $D = (40)^2 - 4(16)(k) = 0$.$1600 - 64k = 0$.$64k = 1600$.$k = \frac{1600}{64} = 25$.Alternatively,for a perfect square of the form $(mx + n)^2 = m^2x^2 + 2mnx + n^2$,we compare $16x^2 + 40x + k$ with $(4x + n)^2 = 16x^2 + 8nx + n^2$.Equating the middle terms: $8n = 40$,so $n = 5$.Then $k = n^2 = 5^2 = 25$.

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

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