Chapter 8, Problem 5CA

To determine

To find: That quadratic functions can have two, one or no real zero.

Answer to Problem 5CA

Yes, He is correct.

Explanation of Solution

Concept used:

  $b^2-4ac>0$ There are two real roots

  $b^2-4ac=0$ There are one real root.

  $b^2-4ac>0$ There are two real roots

Calculation:

Roots are also called x -intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x -axis, or above the x -axis. Therefore, a quadratic function may have one, two, or zero roots.

the roots of a quadratic function are given by,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

This formula is called the quadratic formula, and its derivation is included so that you can see where it comes from. We call the term b² - 4ac the discriminant. The discriminant is important because it tells you how many roots a quadratic function has. Specifically, if

1. If $b^2-4ac<0$, There are no real roots

  

2. $b^2-4ac=0.$ There are one real root..

  

3. $b^2-4ac>0$There are two real roots