Answer:
The roots of the equation are x=-3 and x=-2.5
Step-by-step explanation:
The correct quadratic equation is
2x^2+11x+15=0
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2} +11x+15=0[/tex]
so
[tex]a=2\\b=11\\c=15[/tex]
substitute in the formula
[tex]x=\frac{-11(+/-)\sqrt{11^{2}-4(2)(15)}} {2(2)}[/tex]
[tex]x=\frac{-11(+/-)\sqrt{121-120}} {4}[/tex]
[tex]x=\frac{-11(+/-)\sqrt{1}} {4}[/tex]
[tex]x=\frac{-11(+/-)1} {4}[/tex]
[tex]x_1=\frac{-11(+)1}{4}=-2.5[/tex]
[tex]x_2=\frac{-11(-)1}{4}=-3[/tex]
therefore
The roots of the equation are x=-3 and x=-2.5
