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

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    2021-11-23T12:44:56+00:00

    Answer:

    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.

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