If a- R- b- R- then the equation x2-abx-a2-0 has

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Discriminant

If a∈ R, b∈...

Question

If $a \in R, b \in R$ , then the equation $x^{2} - a b x - a^{2} = 0$ has

one positive root and one negative root

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both root positive

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both root negative

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nonreal roots

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Solution

The correct option is A one positive root and one negative root
$x^{2} - a b x - a^{2} = 0$
Now, $D = a^{2} b^{2} + 4 a^{2}$
Since, $a$ and $b$ are real,
$D > 0$ and roots are real and distinct.
Product of the roots $= - a^{2} < 0$
Therefore, roots are of opposite sign.
Ans: A

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If a∈R,b∈R, then the equation x2−abx−a2=0 has

The correct option is A one positive root and one negative rootx2−abx−a2=0Now, D=a2b2+4a2Since, a and b are real, D>0 and roots are real and distinct.Product of the roots =−a2<0Therefore, roots are of opposite sign.Ans: A

If $a \in R, b \in R$ , then the equation $x^{2} - a b x - a^{2} = 0$ has

The correct option is A one positive root and one negative root
$x^{2} - a b x - a^{2} = 0$
Now, $D = a^{2} b^{2} + 4 a^{2}$
Since, $a$ and $b$ are real,
$D > 0$ and roots are real and distinct.
Product of the roots $= - a^{2} < 0$
Therefore, roots are of opposite sign.
Ans: A