Question 1068617
tell the nature of the solution by using the discriminant and then solve to find the exact root
Factor when Possible

2x^2+7x+3=0
<pre>Discriminant: {{{matrix(1,5, b^2 - 4ac, "=", 7^2 - 4(2)(3), "=", 25)}}}
With the discriminant being a PERFECT SQUARE, then {{{highlight_green(matrix(1,7, 2, "REAL,", "RATIONAL,", and, UNEQUAL, roots, exist))}}}

Now that you have the discriminant, you can continue to solve using the quadratic equation formula, but since the TRINOMIAL can be factored,
it's easier to do so to get the exact roots.
{{{matrix(1,4, 2x^2 + 7x + 3 = 0, factors, to, (2x + 1)(x + 3) = 0)}}}, and we then get: {{{highlight_green(matrix(2,7, 2x + 1, "=", 0, "====>", x, "=", - 1/2, x + 3, "=", 0, "====>", x, "=", - 3))}}}