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

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
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Subinit

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21 hours 2021-11-23T12:43:12+00:00 1 Answer 0

The discriminant is 0

Step-by-step 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.