The solutions to the system of equation f(x) and g(x) are [tex]\frac{3+\sqrt{89}}{4} \ or \ \frac{3-\sqrt{89}}{4}[/tex] and
[tex]\frac{2\sqrt{15}}{3} \ or \ \frac{-2\sqrt{15}}{3}\\[/tex]
Solving quadratic equations
Quadratic equations are equations that has a leading degree of 2. Given the following functions:
f(x)=2x^(2)-3x-10
g(x)=-3x^(2)+20
To solve, we will use the quadratic formula as shown below;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For the quadratic equation f(x)=2x^(2)-3x-10
a = 2
b = -3
c = -10
Substitute
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-10)}}{2(2)}\\x=\frac{3\pm\sqrt{89}}{4}\\x= \frac{3+\sqrt{89}}{4} \ or \ \frac{3-\sqrt{89}}{4}[/tex]
For the quadratic equation -3x² + 20
a =-3
b = 0
c = 20
[tex]x=\frac{0\pm \sqrt{(0)^2-4(-3)(20)}}{2(-3)}\\x=\frac{\pm4\sqrt{15}}{-6}\\x=\frac{2\sqrt{15}}{3} \ or \ \frac{-2\sqrt{15}}{3}\\[/tex]
Learn more on quadratic equations here: https://brainly.com/question/776122
#SPJ1
