Question
If the equation x^{2} − ax + 1 = 0 has two distinct roots, then
|a| = 2
|a| < 2
|a| > 2
None of these
Solution
The given quadric equation is x^{2} − 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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Solution If the Equation X2 − Ax + 1 = 0 Has Two Distinct Roots, Then Concept: Solutions of Quadratic Equations by Factorization.