Question

if x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

Answer 1

Answer:

In a given quadratic equation, The quadratic formula to find the solutions.

x = (-b ± √(b2 - 4ac)) / 2a  

where a, b, and c are coefficients of the equation

ax2 + bx + c = 0  

Since x=6 is the only x-intercept, the equation would be

(x - 6)(x - 6) = 0

By Expanding out, we get x2 - 12x + 36 = 0  

From this equation,

a = 1

b = -12

c = 36

Answer 2

Answer:

D=0

Equal roots

x² - 12x + 36

Step-by-step explanation:

x=6 is the only x-intercept of the graph of a quadratic equation

this means it has equal roots

as it has equal roots so Discriminant would be zero

so Polynomial would be

p(x) = (x-6)(x-6)

=> p(x) = x² - 6x  - 6x + 36

=> p(x) = x² - 12x + 36

Verification

D = b² - 4ac

=> D = (-12)² - 4(1)(36)

=> D = 144 - 144

=> D= 0