Share

# Write the Set of Value of 'A' for Which the Equation X2 + Ax − 1 = 0 Has Real Roots. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.

#### Solution

The given quadric equation is  x2 + 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 > - 4which is true for all real values of a.

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

Is there an error in this question or solution?

#### 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.
S