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

A: The discriminant is 0.

B: The discriminant is 6.

C:The discriminant is negative.

Answer 1

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.

 

 

Your answer is (A).

 

 

 

 

 

Answer 2

There are three things to know:

 

-If the discriminant is 0, there is 1 real solution (indicated by a bounce at the x-axis on the graph)

-If the discriminant is positive, there are 2 real solutions (indicated by crossing the x-axis twice on the graph)

-If the discriminant is negative, there are 2 imaginary solutions (not possible to graph)

 

 

In this case, there is a single, REAL x-intercept

 

This tells us that the discriminant is 0

 

This link may be helpful:

http://www.regentsprep.org/regents/math/algtrig/ate3/discriminant.htm