Zeros and Roots

What are roots and zeros? How are they different?

Functions have zeros and equations have roots. It is important to know that the zeros refer to when the value of \(x\) makes the function equal to zero. In other words, \(y=0\).

Zeros are where the function intercepts the \(x\)-axis.

1. Find the zeros of the following quadratic functions by factorization, inspection, or the quadratic formula.

1. \(f(x)=x^2+2x+4\)
2. \(f(x)=3x^2-2\)
3. \(f(x)=2x^2+5x+4\)
4.  

Graph is created using Desmos.com.

1. Did you find the following zeros:

1. No zeros , used the quadratic formula or could use the graph, does not cross the \(x\)-axis
2. Zeros are \(x = \dfrac{\sqrt{2}}{3}\) and \(x=-\dfrac{\sqrt{2}}{3}\)
3. No zeros , used the quadratic formula or the graph, does not cross the \(x\)-axis
4. \(x\)-intercepts or zeros are:  \((-6,0),(-3,0)\)

2. What strategies do you use for factoring? Once the function had been factored, how did you find the zeros?

Note: If you are having trouble with factoring quadratics, the POLQ modules review factoring of quadratics.

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Go to Practice (Finding Zeros of Rational Numbers)