Graphing questions

Question

Find the values of case so that x²+kx+36=0 will have only one root.

Answer 1

we will use discriminant and roots

when discriminant , D=0 ...it will have only one root

x²+kx+36=0

a=1 , b=k, c= 36

Discriminant = D = k² -4(1)(36)

so k² - 144 =0

(k+12)(k-12)=0

so k = -12 or k=12

Answer 2

A quadratic equation has one root if the discriminant (the part under the radical) = 0.

The term under the radical is b^2 - 4ac, so k^2 - 144 = 0, k^2 = 144, k = +12 or -12.

The equation is either x^2 - 12x + 36 = (x-6)^2 or x^2 +12x + 36 = (x+6)^2, so the root is either 6 or -6.