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Let `f(x)=x^(2)-8kx+16(k^(2)-k+1)` brgt <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_SKG_ALG_C02_E13_016_S01.png" width="80%"> <br> `:.Dgt0` <br> `implies64k^(2)-4.16(k^(2)-k+1)gt0` <br> `implieskgt1` …….i <br> `implies(-b)/(2a)gt4implies(8k)/2gt4` <br> `implieskgt1`………….ii <br> and `f(4)ge0` <br> `implies16-32k+16(k^(2)-k+1)ge0` <br> `impliesk^(2)-3k+2ge0` <br> `implies(k-1)(k-2)ge0` <br> `kle1` or `kge2`...........iii <br> From Eqs i, ii and iii we get <br> `kge2` <br> `k_("min")=2`