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Question
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
Solution
The given quadric equation is 2x2 + kx − 8 = 0 , and roots are real.
Then find the value of k.
Here, a = 2 , b = k and, c = -8
As we know that `D =b^2 - 4ac`
Putting the value of a = 2 , b = k and, c = -8
` = (k)^2 - 4 xx 2 xx (-8)`
= `k^2 + 64`
The given equation will have real roots, if D > 0
I.e., k2 + 64 > 0 which is true for all real values of k
Therefore, for all real values of k, the given equation has real roots.
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