Solve Using the Quadratic Formula 2x^2+3x+5=0

Problem

2*x2+3*x+5=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=2

b=3

c=5

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

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−3±√(,3−4*(2)*(5)))/(2*(2))

4. Simplify the expression inside the square root, which is the discriminant.

x=(−3±√(,9−40))/4

x=(−3±√(,−31))/4

5. Apply the imaginary unit i because the discriminant is negative, where √(,−31)=i√(,31)

x=(−3±i√(,31))/4

Final Answer

x=(−3±i√(,31))/4

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