use the quadratic equation to solve 3x^2+10x+3=0

Question

1.Solve x^2-2x+4=0

2. use the quadratic equation to solve 3x^2+10x+3=0

Answer 1

When using the quadratic equation the most important step is to make sure the equation is set up in the following form:

 

ax^2 +bx + c = 0 

 

 

1. and 2. are already in this form so we are ready to use the quadratic equation:

 

x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

 

 

1. x = [2 ± sqrt(2^2 - 4*1*4)] /(2*1)

 

 x = [2 ± sqrt(-12)] / 2             We see here that there is a negative square root, so the solution is imaginary or you can say there is no real solution.

 

To find the imaginary solution we continue using i = sqrt(-1)

 

so sqrt(-12) = sqrt(-1*12) = i*sqrt(12) = i*sqrt(4*3) = 2*sqrt(3)i.

 

and x = [2 ± 2*sqrt(3)i]/2

 

 

 

2. 3x^2 + 10x + 3 = 0

 

plug into quadratic formula....

 

x = [-10 ± sqrt(10^2 - 4*3*3) ]/2*3

 

x = [-10 ± 8] / 6

 

simplify to: x = -1/3, -3