Question

Determine the greatest intergral value of K for which 2x^2 - Kx +2 =0 will have non-real roots ...Use quadratic inequalities to determine the solution

Answer 1

Greatest integral value of K = 3.

Explanation:

The nature of the roots of a quadratic equation is determined by the sign of the discriminant, b^2 - 4ac. For non-real roots this is negative.

2x^2 - kx + 9 = 0

The discriminant = (-k)^2 - 4*2*2 , so:

k^2 - 16 < 0 for non-real roots.

k^2 < 16

k < √16

k < 4

So the answer is 3.

The greatest integral value is 8.