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Question

If both the roots of the quadratic equation ax2+bx+c=0 are negative, then

A
a,b,c can be any negative integers
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B
a,b,c can be any positive rational numbers
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C
a,b,c can be any real numbers
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D
a,b,c can be any integers
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Solution

The correct options are
A a,b,c can be any negative integers
B a,b,c can be any positive rational numbers
As both the roots are negative, so
α+β<0ba<0ba>0(1)α×β>0ca>0(2)

When a>0, using equation (1) and (2), we get
b>0, c>0
Similarly, when a<0, using equation (1) and (2), we get
b<0, c<0

Hence, a,b,c has to be of same sign.

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