Question

Find the zeros for the quadratic function below. Write your answer in fractional form if necessary. Do not use decimals.

Answer 1

Step1: Write out the equation

`f(x)=-3x^2-4x+7`

Apply quadratic formula method

Step2: write out the quadratic formula

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Step3: Identify the variable

from the function giving, compared with the general form of a quadratic equation

`\begin{gathered} f(x)=ax^2+bx+c \\ \text{Then} \\ a=-3,b=-4,c=7 \end{gathered}`

Step4; Substitute the value of each variable into the formula

`x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(-3)(7)}}{2(-3)}`

Step5: simplify the equation above

`\begin{gathered} x=\frac{4\pm\sqrt[]{16+84}}{-6} \\ \\ x=\frac{4\pm\sqrt[]{10}}{-6} \\ \end{gathered}`

Then, we have

`\begin{gathered} x=(4\pm10)/(-6) \\ \\ x=(4+10)/(-6),(4-10)/(-6) \\ \\ x=(14)/(-6),(-6)/(-6) \end{gathered}`

Therefore the value of x are

`\begin{gathered} x=-(7)/(3),1 \\ \text{Then } \\ x=-(7)/(3),\text{ and 1} \end{gathered}`

Therefore

Blank 1=-7/3

Blank 2=1