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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 > - 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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