Solve the quadratic equation 3x^2 - 11x + 21 = 0 using the quadratic formula.

Answer 1

We have the equation 3x^2 - 11x +21 - 0 which is in standard form for a quadratic equation. In general the standard form is:

Ax^2 + Bx + C = 0

We can identify

A = 3, B = -11, C = 21

The solution to the standard form is:

x = {-B +/- sqrt(B^2 - 4 * A * C) } / 2A

Substituting our known values we have:

x = {11 +/- sqrt(121 - 4 * 3 * 21) } / 6 = 11/6 +/- sqrt(-131)/6 = 1.83 +/- 1.91i

The two solutions are therefore x = 1.83 + 1.91i and 1.83 - 1.91i

Lets check the first one:

x = 1.83 + 1.91i => 3*(1.83+1.91i)^2 - 11*(1.83+1.91i) +21 = 3*(3.35 + 6.99i - 3.65) - 20.1 -21.0i + 21 = 0

Answer 2

3x² -11x +21 = 0 here a= 3 b=-11 c=21 x= ( - b ±√ ( b²- 4 ac) )/ 2a using this x = (11±√(121- 252))/6

x=11/6 ± √ -131/6 x= 1.833 ± 1.9081i where i = √-1