For what value(s) of k will the function f(x) = 2x^2 – kx + 18 have: a) have 2 equal roots b) two non real roots

Answer 1

Lets say we have an equation 0=x²+6x+9. We can solve this by factoring as a perfect square trinomial, so 0=(x+3)²→x=−3 and -3. Hence, there will be two identical solutions.The discriminant of the quadratic equation (b²−4ac) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have 2 equal, or 1 distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:

k²−(4×2×18)=0

k²−144=0

(k+12)(k−12)=0

k=±12

So, k can either be 12 or −12.