The general equation of a quadratic equation is given by
[tex]y=ax^2+bx+c[/tex]The solution to the equation, using the formula method is given by
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]To solve the question, we will apply the formula above to match the options provided
Step1: Match
[tex]2x^2-8x+5=0[/tex]In this case, a=2, b=-8, c=5
substituting into the formula
we will obtain
[tex]\frac{8\pm\sqrt[]{24}}{4}[/tex]simplifying further
Upon factoring out 2
We will obtain:
[tex]\frac{4\pm\sqrt[]{6}}{2}[/tex]Step2: Match
[tex]2x^2-10x-3=0[/tex]In this case,
a=2, b=-10 and c =-3
substituting into the quadratic formula
we will obtain
[tex]\frac{10\pm2\sqrt[]{19}}{4}[/tex]simplifying further
we will obtain
[tex]\frac{5\pm\sqrt[]{19}}{2}[/tex]Step 3: Match
[tex]2x^2-8x-3=0[/tex]In this case: a=2, b=-8 and c=-3
substituting into the quadratic formula
we will obtain
[tex]\frac{8\pm2\sqrt[]{22}}{4}[/tex]Simplifying further
we will obtain
[tex]\frac{4+\sqrt[]{22}}{2}[/tex]Step 4: Match
[tex]2x^2-9x-1=0[/tex]In this case: a=2, b=-9 and c =-1
substituting into the quadratic formula
we will obtain
[tex]\frac{9+\sqrt[]{89}}{4}[/tex]Step 5: Match
[tex]2x^2-9x+6=0[/tex]