Question

find the zeros of the function $f(x)=-1.3x^{2}+11.5x - 21$. round values to the nearest thousandth (if necessary).

Explanation:

Step1: Set the function equal to zero

$-1.3x^{2}+11.5x - 21=0$

Step2: Use the quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$, the solutions are $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=-1.3$, $b = 11.5$, and $c=-21$.
First, calculate the discriminant $\Delta=b^{2}-4ac=(11.5)^{2}-4\times(-1.3)\times(-21)$
$=132.25-109.2=23.05$

Step3: Find the two solutions

$x_1=\frac{-11.5+\sqrt{23.05}}{2\times(-1.3)}=\frac{-11.5 + 4.801}{-2.6}=\frac{-6.699}{-2.6}\approx2.576$
$x_2=\frac{-11.5-\sqrt{23.05}}{2\times(-1.3)}=\frac{-11.5 - 4.801}{-2.6}=\frac{-16.301}{-2.6}\approx6.270$

Answer:

$x\approx2.576$ and $x\approx6.270$