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प्रश्न
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
विकल्प
2
– 2
`(1)/(4)`
`(1)/(2)`
उत्तर
If `(1)/(2)` a root of the equation `x^2 + kx - 5/4 = 0`, then the value of k is 2.
Explanation:
`(1)/(2)` is a root of the equation
x2 + kx – `(5)/(4)` = 0
Substituting the value of x = `(1)/(2)` in the equation
`(1/2)^2 + k xx (1)/(2) - (5)/(4)` = 0
⇒ `(1)/(4) + k/(2) - (5)/(4)` = 0
⇒ `k/(2) - 1` = 0
⇒ k = 1 × 2 = 2
∴ k = 2
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Solution :
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∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
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∴ The roots of the equation are real and unequal.
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