#### Question

Write the set of value of 'a' for which the equation x^{2} + ax − 1 = 0 has real roots.

#### Solution

The given quadric equation is x^{2} + ax − 1 = 0

Then find the value of *a.*

Here, a= 1, b = a and, c = -1

As we know that `D = b^2 - 4ac`

Putting the value of a= 1, b = a and, c = -1

` = (a)^2 - 4 xx 1 xx -1`

` = a^2 + 4`

The given equation will have real roots, if D > 0_{.}

`a^2 + 4 >0`

⇒ `a^2 > - 4`which is true for all real values of a.

Therefore, for all real values of a, the given equation has real roots.

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#### APPEARS IN

Solution Write the Set of Value of 'A' for Which the Equation X2 + Ax − 1 = 0 Has Real Roots. Concept: Solutions of Quadratic Equations by Factorization.