Find the Roots (Zeros) 2x^2-4x+9=0

Problem

2*x2−4*x+9=0

Solution

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

a=2

b=−4

c=9

2. Apply the quadratic formula to solve for x

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(−4)±√(,(−4)2−4*(2)*(9)))/(2*(2))

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

x=(4±√(,16−72))/4

x=(4±√(,−56))/4

5. Simplify the radical using the imaginary unit i where √(,−1)=i

√(,−56)=√(,−1⋅4⋅14)

√(,−56)=2*i√(,14)

6. Substitute the simplified radical back into the equation.

x=(4±2*i√(,14))/4

7. Divide each term in the numerator by the denominator to find the final roots.

x=4/4±(2*i√(,14))/4

x=1±(i√(,14))/2

Final Answer

x=1±(i√(,14))/2

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