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Question
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
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Solution
The given quadric equation is 3x2 + 2x + k = 0, and roots are real.
Then find the value of k.
Here, a = 3, b = 2 and c = k
As we know that D = b2 - 4ac
Putting the value of a = 3, b = 2 and c = k
= (2)2 - 4 x (3) x (k)
= 4 - 12k
The given equation will have real roots, if D ≥ 0
4 - 12k ≥ 0
12k ≤ 4
k ≤ 4/12
k ≤ 1/3
Therefore, the value of k ≤ 1/3
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