Question

Please help:What are the zeros of the quadratic function?f (z )= 3z^2 − 11z − 4Enter your answers, as simplified fractions if necessary, in the boxes.The zeros of f (z) are __ and __.

Answer 1

We need to find the zeros for the next function:

`f(z)=3z^2−11z−4`

We can find those zeros using the quadratic formula given by:

`x=(-b\pm√(b^2-4ac))/(2a)`

Use the form ax²+bx+x.

Where a=3

b= -11

c=-4

Replacing :

`\begin{gathered} x=(-(-11)\pm√((-11)^2-4(3)(-4)))/(2(3)) \\ Simplify \\ x=(11\pm√(169))/(2\ast3) \\ x=(11\pm13)/(2\ast3) \\ Therefore: \\ x_1=(11-13)/(6)=(-2)/(6)=-(1)/(3) \\ x_2=(11+13)/(6)=(24)/(6)=4 \end{gathered}`

Therefore, the zeros of f (z) are -1/3 and 4.