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प्रश्न
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
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उत्तर
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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संबंधित प्रश्न
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Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
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Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
