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Question
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Solution
The given quadric equation is x2 + kx + 4 = 0, and roots are real.
Then find the value of k.
Here,
a = 1, b = k and c = 4
As we know that D = b2 − 4ac
Putting the value of a = 1, b = k and c = 4
= k2 − 4 × (1) × (4)
= k2 − 16
The given equation will have real and equal roots, if D = 0
k2 − 16 = 0
Now factorizing of the above equation
k2 − 16 = 0
k2 = 16
`k=sqrt16`
k = ± 4
Now according to question, the value of k is positive.
Therefore, the value of k = 4
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