x<−32 or x>5
x<−5 or x>32
−32<x<5
−5<x<32
Correct answer is B
2x2+7x−15>0⟹2x2−3x+10x−15>0
x(2x−3)+5(2x−3)>0
(x+5)(2x−3)>0
For their product to be positive, they are either both +ve or -ve.
x+5>0⟹x>−5
2x−3>0⟹2x>3
x>32
Check:
x>−5:x=−3
2(−3)2+7(−3)−15=18−21−15=−18<0 (Not satisfied)
∴
x > \frac{3}{2}: x = 2
2(2^{2}) + 7(2) - 15 = 8 + 14 - 15 = 7 > 0 (Satisfied)
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