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?
The discriminant is 0.
The discriminant is 6.
The discriminant is positive
The discriminant is negative
Mark this and return
Save and Exit
Next
Subinit

Answer 1

The discriminant is 0

Explanation:

In a quadratic equation , we use 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

Expanding this out, we get

x2 - 12x + 36 = 0

In this equation,

a = 1

b = -12

c = 36

Now the discriminant is the square-root part of the formula:

b2 - 4ac

Now plug in the values of a,b, and c into the discriminant.

(-12)2 - 4(1)(36) = 144 - 144 = 0

This number is under the square-root. The square-root of 0 is 0.