Solve Using the Quadratic Formula 4x^2-5x+2=0

Problem

4*x2−5*x+2=0

Solution

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

a=4

b=−5

c=2

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

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(−5)±√(,(−5)2−4*(4)*(2)))/(2*(4))

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

x=(5±√(,25−32))/8

x=(5±√(,−7))/8

5. Apply the imaginary unit i because the discriminant is negative, where √(,−7)=i√(,7)

x=(5±i√(,7))/8

Final Answer

x=(5±i√(,7))/8

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