Question

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
The discriminant is negative.
The discriminant is –3.
The discriminant is 0.
The discriminant is positive.

Answer 1

Answer:it is negative

Step-by-step explanation:

Answer 2

The statement best describes the discriminant of the equation, is that "The discriminant is 0". (option 3rd)

Given,

The only x-intercept of the graph of a quadratic equation is x = -3.

To find,

The statement, among the given ones, best describes the discriminant of this equation.

Solution,

The x-intercept of a quadratic equation is given to be x = -3.

Also, it is the only x-intercept of this equation.

Now, as we know that the x-intercept is also the root of the quadratic equation.

Here, since the graph cuts the x-axis at only one point, i.e. x = -3.

⇒ x = -3 is the only root of the equation.

Thus, the given quadratic equation has real and equal roots.

Now, the condition for a quadratic equation to have equal roots is that its discriminant is equal to 0. That is,

$D=0$

Therefore, the statement best describes the discriminant of the equation, is that "The discriminant is 0". (option 3rd)

#SPJ3