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Question

# For the given quadratic equation y=âˆ’x2âˆ’5xâˆ’4,y<0 for

A
x(,1)(4,)
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B
x(,4)(1,)
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C
x(4,1)
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D
x(1,4)
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Solution

## The correct option is B x∈(−∞,−4)∪(−1,∞)Given: y=−x2−5x−4 On comparing with the standard quadratic expression y=ax2+bx+c, we get a=−1,b=−5,c=−4. And we know, D=b2−4ac=(−5)2−4(−1)(−4) D=9>0 ⇒ the equation will have two distinct roots. Which will be: x=−(−5)±√9−2⇒x=5+3−2 or x=5−3−2⇒x=−4 or x=−1 Now a<0⇒ parabola will be downward opening; and D>0⇒ parabola will cut the x-axis at two distinct points. ∴ the graph of the given expression can be drawn as: And given expression is negative for x=(−∞,−4)∪(−1,∞)

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