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Question
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
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Solution
Given quadratic equation is 4x2 + 8x – k = 0 ...(i)
The quadratic equation has real roots if its discriminant is greater than or equal to zero
`=>` D = b2 – 4ac ≥ 0
`=>` 82 – 4(4)(–k) ≥ 0
`=>` 64 + 16k ≥ 0
`=>` 16k ≥ – 64
`=>` k ≥ – 4
Hence, the given quadratic equation has real roots for k ≥ – 4.
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