Q5. - Algebra 1

Question

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.

Step-by-Step Solution

Answer

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 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

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

The $x$-intercepts of a function $y=a{x}^2+bx+c$ are the points, where the value $y$ is equal to 0. 

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

If the graph of the quadratic equation $y=a{x}^2+bx+c,$ 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.