The number of integral values of $x$ for which $f (x) = 2 x^{2} - 20 x + 42$ is negative is

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Solution

$f (x) = 2 x^{2} - 20 x + 42$
Now,
$f (x) = 0 \Rightarrow 2 x^{2} - 20 x + 42 = 0 \Rightarrow x^{2} - 10 x + 21 = 0 \Rightarrow (x - 3) (x - 7) = 0 \Rightarrow x = 3, 7$

The graph of the $f (x)$ is

Therefore $f (x)$ is negative for $x \in (3, 7)$
Hence, the number of integral value is $3.$

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