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in Quadratic Equations by (34.1k points)
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The roots of each of the following quadratic equations are real and equal, find k.

i. 3y2 + ky + 12 = 0 

ii. kx (x-2) + 6 = 0

1 Answer

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i. 3y2 + kg + 12 = 0

Comparing the above equation with

Since, the roots are real and equal.

∴ ∆ = 0 

∴ (k + 12) (k – 12) = 0 

∴ k + 12 = 0 or k – 12 = 0 

∴ k = -12 or k = 12

ii. kx (x – 2) + 6 = 0 

∴ kx2 – 2kx + 6 = 0

Comparing the above equation with

Since, the roots are real and equal.

∴ ∆ = 0 

∴ 4k (k – 6) = 0 

∴ k(k – 6) = 0 

∴ k = 0 or k – 6 = 0

But, if k = 0 then quadratic coefficient becomes zero. 

∴ k ≠ 0 

∴ k = 6

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