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

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Nature of Roots

If a,b ∈ R ...

Question

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

One positive and one negative root

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Both positive root

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Both negative root

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Non-real root

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Solution

The correct option is A One positive and one negative root
Roots of the given equation are : $\frac{a b \pm \sqrt{b^{2} + 4}}{2}$

Roots = $a \frac{(b \pm \sqrt{b^{2} + 4)}}{2}$

Given $a, b \in R$

Here $\sqrt{b^{2}} = b < \sqrt{b^{2} + 4}$

$∴$ one root is positive and one root is negative

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

The correct option is A One positive and one negative rootRoots of the given equation are :ab±√b2+42Roots =a(b±√b2+4)2Given a,b∈RHere √b2=b<√b2+4∴one root is positive and one root is negative

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

The correct option is A One positive and one negative root
Roots of the given equation are : $\frac{a b \pm \sqrt{b^{2} + 4}}{2}$

Roots = $a \frac{(b \pm \sqrt{b^{2} + 4)}}{2}$

Given $a, b \in R$

Here $\sqrt{b^{2}} = b < \sqrt{b^{2} + 4}$

$∴$ one root is positive and one root is negative