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प्रश्न
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
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उत्तर
`3"x"^2 – 12"x" + (n – 5) = 0`
Here a = 3, b = − 12 and c = n – 5
Given: equation has equal roots
Then D = 0
⟹ `"b"^2 – 4"ac" = 0`
⟹ `[− 12]^2 – 4(3)("n" – 5) = 0`
⟹ 144 – 12n + 60 = 0
⟹ − 12n = − 204
⟹ `"n"=(-204)/-12=17`
संबंधित प्रश्न
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Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
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a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
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∴ The roots of the equation are real and unequal.
