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State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

A quadratic equation with a graph that has two x-intercepts has one real root.

Short Answer

Expert verified

The sentence, “The quadratic equation with a graph that has two x-intercepts has one real root ” is false.

The correct replacement for the underlined term to make a true sentence is two.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, y=ax2+bx+c, where, a0is called the standard form of the quadratic function.

02

Step 2. Define the x-intercept of a function.

The x-intercepts of a function y=ax2+bx+c are the points, where the valuey is equal to 0.

03

Step 3. Check whether the given sentence is true or false.

If the graph of the quadratic equation y=ax2+bx+c,has two intercepts, then it means that the graph cuts the -axis at two points and the equation has two real roots.

Therefore, the sentence, “The quadratic equation with a graph that has two x-intercepts has one real root ” is false.

The correct replacement for the underlined term to make a true sentence is two.

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