Posted by janet on Monday, November 26, 2012 at 5:56am.
2x^2 + 6x +3 = 0
That does not factor into terms with integers. Use the quadratic formula
x= [-b +/-sqrt(b^2-4ac)]/2a
x = [-6 +/-sqrt(36 -24)]/4
= [-6 +/-sqrt12]/4
= -2.366 or -0.634
2 x ^ 2 + 6 x + 3 = 0
Compare your equation to the standard form :
a x ^ 2 + b x + c = 0
and identify the values for a , b , c.
a = 2
b = 6
c = 3
Now evaluate the discriminant :
b ^ 2 - 4 a c = 6 ^ 2 - 4 * 2 * 3 = 36 -
24 = 12
Since b ^ 2 - 4 ac > 0 there are two unequal real solutions:
x1 = [ - b + sqrt ( b ^ 2 - 4 a c ) ] / 2 a
x1 = [ - 6 + sqrt ( 12 ) ] / 2 * 2
x1 = [ - 6 + sqrt ( 4 * 3 ) ] / 4
x1 = [ - 6 + 2 * sqrt ( 3 ) ] / 4
x1 = 2 * [ - 3 + sqrt ( 3 ) ] / 2 * 2
x1 = [ - 3 + sqrt ( 3 ) ] / 2
x1 = [ sqrt ( 3 ) - 3 ] / 2
x1 = - 0.63 approx.
x2 = [ - b - sqrt ( b ^ 2 - 4 a c ) ] / 2 a
x2 = [ - 6 - sqrt ( 12 ) ] / 2 * 2
x2 = [ - 6 - sqrt ( 4 * 3 ) ] / 4
x2 = [ - 6 - 2 * sqrt ( 3 ) ] / 4
x2 = 2 * [ - 3 - sqrt ( 3 ) ] / 2 * 2
x2 = [ - 3 - sqrt ( 3 ) ] / 2
x2 = [ - 3 - sqrt ( 3 ) ] / 2
x2 = - 2.37 approx.