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Question
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
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Solution
The given quadric equation is 2x2 + kx + 2 = 0, and roots are real.
Then find the value of k.
Here, a = 2, b = k and c = 2
As we know that D = b2 - 4ac
Putting the value of a = 2, b = k and c = 2
= k2 - 4 x (2) x (2)
= k2 - 16
The given equation will have real roots, if D ≥ 0
⇒ k2 - 16 ≥ 0
⇒ k2 ≥ 16
`rArrk>=sqrt16`Or `k <=-sqrt16`
⇒ k ≥ 4 Or k ≤ -4
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