Answer:
(2,0)
Step-by-step explanation:
Given:
The equation is given as: [tex]y=-3x^{2}+5x+2[/tex]
For x intercept, [tex]y=0[/tex].
Therefore, [tex]-3x^{2}+5x+2=0[/tex]
Now, comparing this with the standard quadratic equation [tex]ax^{2}+bx+c=0[/tex], we get
[tex]a=-3,b=5,c=2[/tex]
Now, using quadratic formula for the above equation,
[tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\\x=\frac{-5 \pm \sqrt{5^{2}-4(-3)(2)}}{2(-3)}\\x=\frac{-5 \pm \sqrt{25+29}}{-6}\\x=\frac{-5 \pm \sqrt{49}}{-6}\\x=\frac{-5 \pm 7}{-6}\\x=\frac{-5-7}{-6}\textrm{ or }x=\frac{-5+7}{-6}\\x=\frac{-12}{-6}\textrm{ or }x=\frac{2}{-6}\\x=2\textrm{ or }x=-\frac{1}{3}=-0.33[/tex]
Therefore, there are two x intercepts. One was given as (-0.33,0). So, the other one is (2, 0).
