If x be real, then maximum value of 5 + 4x - 4{x^2} will be equal to

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4-2.Quadratic Equations and Inequations

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If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to

A

$5$

B

$6$

C

$1$

D

$2$

Solution

(b) Let $f(x) = 5 + 4x – 4{x^2} = y\,\,\,\, \Rightarrow \,\,4{x^2} – 4x – 5 + y = 0$

Since $x$ is real, so ${B^2} – 4AC \ge 0$

==> $16 – 4.4( – 5 + y) \ge 0$

==> $16 – 16( – 5 + y) \ge 0\,\, \Rightarrow \,\, – 5 + y \le 1\,\, \Rightarrow y \le 6$

Hence maximum value of $y$ is $6$.

Standard 11

Mathematics

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