Solve the following equation:

Question

x^3 - 7x^2 + 3x=0

Answer 1

The equation is x^3 - 7x^2 + 3x = 0.

By factor by grouping

x(x^2 - 7x + 3)= 0

Apply zero product property.

x = 0 and x^2 - 7x + 3 = 0

x^2 - 7x + 3 = 0, is a quadratic, use quadratic formula to find roots of the related quadratic equation.

x = [ - b ± √(b^2 - 4ac) ]/2a.

Compare the above equation with standard form of the quadratic equation ax^2 + bx + c = 0.

Substitute the values of a = 1, b = - 7, and c = 3 in x = [ - b ± √(b^2 - 4ac) ]/2a.

x = [ - (- 7) ± √((- 7)^2 - 4(1)(3)) ]/2(1)

x = [ 7 ± √(49 - 12) ]/2

x = [ 7 ± √37 ]/2.

x = [ 7 + √37 ]/2 and x = [ 7 - √37 ]/2.

The solutions of the equation are x = 0, x = [ 7 + √37 ]/2 and x = [ 7 - √37 ]/2.