For the quadratic equation to have equal roots, the discriminant must be zero. Th discriminant ∆ for the equation ax2+bx+c=0 is given by: ∆=b2−4ac Here, a=1,b=2(K+2), and c=36. Thus, the discriminant is: ∆=(2(K+2))2−4×1×36=0. Simplifying:
K+2=6‌‌⇒‌‌K=4,‌‌ or ‌‌K+2=−6‌‌⇒‌‌K=−8.
Thus, K=4 or K=−8. Quick Tip For a quadratic equation to have equal roots, the discriminant must be zero. Use the formula ∆=b2−4ac to solve for the unknown.