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For what value of k the quadratic polynomial 3z2 + 5z + k can be factored into product of real linear factors ?
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k ≤ 25 6 -
k ≤ 25 12 -
k ≥ 25 12 -
k ≥ 25 6
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Correct Option: B
We have , the given quadratic eq. 3z 2 + 5z + k
Comparing it with ax 2 + bx + c = 0, we get a = 3, b = 5, c = k
Now , D = b2 - 4ac = 25 - 12k
For equal linear factors to exist, D ≥ 0
⇒ 25 - 12k ≥ 0
⇒ 25 ≥ 12k
| ⇒ k ≤ | |
| Therefore, the set of real numbers ≤ | gives the set of value of k for which the given | |
