The set of values of x in R satisfying the in | vedclass

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(B) To solve the inequality $x^2 - 4x - 21 \leq 0$,we first find the roots of the quadratic equation $x^2 - 4x - 21 = 0$.Using the quadratic formula $

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$[-3, 7]$

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(B) To solve the inequality $x^2 - 4x - 21 \leq 0$,we first find the roots of the quadratic equation $x^2 - 4x - 21 = 0$.Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$,where $a = 1, b = -4, c = -21$:$x = \frac{4 \pm \sqrt{(-4)^2 - 4(1)(-21)}}{2(1)}$$x = \frac{4 \pm \sqrt{16 + 84}}{2} = \frac{4 \pm \sqrt{100}}{2} = \frac{4 \pm 10}{2}$So,$x_1 = \frac{14}{2} = 7$ and $x_2 = \frac{-6}{2} = -3$.The inequality can be written as $(x - 7)(x + 3) \leq 0$.For the product to be less than or equal to zero,$x$ must lie between the roots inclusive.Thus,$x \in [-3, 7]$.

The set of values of $x \in R$ satisfying the inequality $x^2 - 4x - 21 \leq 0$ is

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