Solve Using the Quadratic Formula r^2+3r+2=0

Problem

r2+3*r+2=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*r2+b*r+c=0

a=1

b=3

c=2

2. State the quadratic formula used to find the roots of the equation.

r=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

r=(−3±√(,3−4*(1)*(2)))/(2*(1))

4. Simplify the expression inside the square root (the discriminant).

r=(−3±√(,9−8))/2

r=(−3±√(,1))/2

r=(−3±1)/2

5. Solve for the two possible values of r by evaluating the plus and minus cases.

(r_1)=(−3+1)/2=(−2)/2=−1

(r_2)=(−3−1)/2=(−4)/2=−2

Final Answer

r=−1,−2

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