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

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Question

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

Options
  • |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?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 2 | Page no. 83
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 2 | Page no. 83
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If the Equation X2 − Ax + 1 = 0 Has Two Distinct Roots, Then Concept: Solutions of Quadratic Equations by Factorization.
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