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# If the Equation X2 − Ax + 1 = 0 Has Two Distinct Roots, Then - CBSE Class 10 - Mathematics

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ConceptSolutions of Quadratic Equations by Factorization

#### Question

If the equation x2 − ax + 1 = 0 has two distinct roots, then

• |a| = 2

• |a| < 2

• |a| > 2

• None of these

#### Solution

The given quadric equation is x2 − ax + 1 = 0 , and roots are distinct.

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 and distinct roots, if D > 0

a^2-  4 > 0

a^2 > 4

 a > 4

a > sqrt4

> ± 2

Therefore, the value of |a| > 2.

Is there an error in this question or solution?

#### APPEARS IN

Solution If the Equation X2 − Ax + 1 = 0 Has Two Distinct Roots, Then Concept: Solutions of Quadratic Equations by Factorization.
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