Find the Roots (Zeros) f(x)=2x^2-7x-30

Problem

ƒ(x)=2*x^2−7*x−30

Solution

1. Set the function to zero to find the roots of the quadratic equation.

2*x^2−7*x−30=0

2. Identify the coefficients a b and c for use in the quadratic formula or factoring.

a=2

b=−7

c=−30

3. Find two numbers that multiply to a⋅c=−60 and add to b=−7

−12⋅5=−60

−12+5=−7

4. Rewrite the middle term using the numbers found in the previous step to factor by grouping.

2*x^2−12*x+5*x−30=0

5. Factor by grouping by taking the greatest common factor out of each pair of terms.

2*x*(x−6)+5*(x−6)=0

(2*x+5)*(x−6)=0

6. Apply the zero product property by setting each factor equal to zero and solving for x

2*x+5=0⇒x=−5/2

x−6=0⇒x=6

Final Answer

x=−5/2,6

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