Question

9. For what value of 'q', 4x4+12x3+25x2+24x+q. will be a perfect square?​

Answer 1

$\textbf{Given:}$

$\mathsf{4x^4+12x^3+25x^2+24x+q\;is\;a\;perfect\;square}$

$\textbf{To find:}$

$\textsf{The value of q}$

$\textbf{Solution:}$

$\mathsf{Since\;4x^4+12x^3+25x^2+24x+q\;is\;a\;perfect\;square,\;we\;can\;write}$

$\mathsf{4x^4+12x^3+25x^2+24x+q=(2x^2+lx+m)(2x^2+lx+m)}$

$\textsf{Equating coefficient of 'x' on bothsides, we get}$

$\mathsf{24=2\;lm}$

$\implies\mathsf{lm=12}$-------(1)

$\mathsf{Equating\;coefficient\;of\;x^3\;on \;bothsides,\;we\;get}$

$\mathsf{12=4\,l}$

$\mathsf{l=\dfrac{12}{4}}$

$\implies\boxed{\mathsf{l=3}}$

$\mathsf{Put\;l=3\;in\;(1),}$

$\mathsf{3m=12}$

$\mathsf{m=\dfrac{12}{3}}$

$\implies\boxed{\mathsf{m=4}}$

$\mathsf{Also,}$

$\mathsf{q=m^2}$

$\mathsf{q=4^2}$

$\implies\boxed{\mathsf{q=16}}$

$\textbf{Find more:}$

The value of n for which the expression x^4+4x^3+nx^2+4x+1 becomes a perfect square

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Answer 2

Step-by-step explanation:

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