Question

The set of values of x for which the inequalities
${x}^{2} - 3x - 10 < 0$
and
$10x - {x}^{2} - 16 > 0$
hold simultaneously is
a) (-2,5)
b) (2,8)
c) (-2,8)
d) (2,5)​

Answer 1

Step-by-step explanation:

We have,

x

2

−3x−10<0

⇒(x−5)(x+2)<0

⇒−2<x<5

Also,

10x−x

2

−16>0

x

2

−10x+16<0

(x−2)(x−8)<0

Hence, 2<x<8

The common set for x is (2,5).

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