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Question

For the quadratic equation ax2+bx+c=0, a,b,cR if b24ac>0 and ac>0, then which of the following is always true ?

A
Roots are of same sign
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B
Roots are of opposite sign
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C
Roots are always negative
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D
Roots are always positive
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Solution

The correct option is A Roots are of same sign
ax2+bx+c=0, a,b,cR
Given b24ac>0
and ac>0
Since, a0
Dividing by a2 both the sides, we get
ca>0
Product of roots is greater than 0.
Hence, roots are of same sign.

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