Question

use the aleks graphing calculator to find all the real zeros of the quadratic function.
$f(x)=2x^{2}+3x-6$
round to the nearest hundredth.
if there is more than one answer, separate them with commas.
if there are no real zeros, click on
one\.
real zero(s):

Explanation:

Step1: Recall quadratic formula

For $ax^2+bx+c=0$, zeros are $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step2: Identify coefficients

Here $a=2$, $b=3$, $c=-6$

Step3: Calculate discriminant

$\Delta = b^2-4ac = 3^2-4(2)(-6) = 9 + 48 = 57$

Step4: Compute first zero

$x_1=\frac{-3+\sqrt{57}}{2(2)}=\frac{-3+7.55}{4}=\frac{4.55}{4}=1.14$

Step5: Compute second zero

$x_2=\frac{-3-\sqrt{57}}{2(2)}=\frac{-3-7.55}{4}=\frac{-10.55}{4}=-2.64$

Answer:

1.14, -2.64