First slide

Theory of expressions

Question

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

Moderate

A

5
B

6
C

1
D

2

Solution

Let $f (x) = 5 + 4 x - 4 x^{2} = y \Rightarrow 4 x^{2} - 4 x - 5 + y = 0$
Since x is real, so $B^{2} - 4 AC \geq 0$
$\Rightarrow 16 - 4.4 (- 5 + y) ⩾ 0$
$\Rightarrow 16 - 16 (- 5 + y) ⩾ 0 \Rightarrow - 5 + y \leq 1 \Rightarrow y \leq 6$
Hence maximum value of y is 6.

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