The graph of an equation with a negative discriminant always has which characteristic?

A. no x-intercept

B. no y-intercept

C. no maximum

D. no minimum

Answer

A quadratic equation with a negative discriminant indicates that the graph does not intersect the x-axis, meaning there are no real solutions. Therefore, the correct answer is that it has no x-intercept. Thus, the correct choice is option A.

To understand the characteristics of a quadratic equation's graph concerning its discriminant, we need to look at what the discriminant tells us. The discriminant, denoted as Δ, is calculated using the formula:

Δ=b2−4ac

where the quadratic equation is in the standard form ax2 +bx+c=0 with a=0.

The discriminant informs us about the nature of the roots (solutions) of the quadratic equation:

When the discriminant is negative, this indicates that the quadratic equation has complex (imaginary) solutions, which means the parabola does not intersect the x-axis at any point. Therefore, a graph of such a quadratic equation will not have any x-intercepts.

In summary, for a quadratic equation with a negative discriminant:

Thus, the correct choice from the options provided is:

A. no x-intercept.

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