Find the least integral value of k ...
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Find the least integral value of k for which the equation x^2 -2(k+2)x + 12 + k^2 = 0 has two different real roots.

JEE/Engineering Exams
Maths
Solution
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Find the least integral value of k for which the equation x^2 -2(k+2)x + 12 + k^2 = 0 has two different real roots.
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X^2-2(k+2)x+12+k^2=0

I ≥ 0

[2(k+2)]-4×(12+k^2)>0

4.(k^2+4+4k)-48-4k^2>0

16+16K-48>0

16-32>0

(k-2)>0

k>2

Least integral value = 3

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