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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $k = \ldots$

Similar Questions

Examine whether the following equation is quadratic or not: $(2x + 1)(3x + 2) = 6(x - 1)(x - 2)$

State whether the quadratic equation $(x-1)(x+2)+2=0$ has two distinct real roots. Justify your answer.

Examine whether the following equation is quadratic or not: $x + \frac{1}{x} = x^2$ $(x \neq 0)$

Which of the following polynomials does not have any real zero?

The value of discriminant $D$ of the quadratic equation $25x^{2} - 10x + 1 = 0$ is ..... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module