Question

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

The solutions of a quadratic equation are called roots.

Short answer

The sentence, “The solutions of a quadratic equation are called roots” is true.

Step-by-step solution

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

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

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 of$y$ is equal to 0.

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

The values of $x$ that satisfy the quadratic equation $a{x}^2+bx+c=0$ are called the roots.

It means that the $x$-intercepts of a quadratic function $y=a{x}^2+bx+c$are called the roots of the quadratic equation $a{x}^2+bx+c=0$

Therefore, the sentence, “The solutions of a quadratic equation are called roots” is true.