Question

Find the zeros of each functions by using a graph and a table. F(x)=5x^2-15x+10

Answer 1

We have to find the zeros of f(x):

`\begin{gathered} f(x)=5x^2-15x+10=0 \\ 5(x^2-3x+2)=0 \\ x^2-3x+2=0 \end{gathered}`

We apply then the quadratic equation:

`\begin{gathered} x=(-b)/(2a)\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ \\ x=(-(-3))/(2\cdot1)\pm\frac{\sqrt[]{(-3)^2-4\cdot1\cdot2}}{2\cdot1} \\ \\ x=(3)/(2)\pm\frac{\sqrt[]{9-8}}{2}=(3)/(2)\pm\frac{\sqrt[]{1}}{2}=(3)/(2)\pm(1)/(2) \\ \\ x_1=(3)/(2)+(1)/(2)=(4)/(2)=2 \\ x_2=(3)/(2)-(1)/(2)=(2)/(2)=1 \end{gathered}`

The zeros of the function are x1=2 and x2=1.