Question

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.

Solution

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**