The discriminant is b2 - 4ac. In this case, a = 1, b = 7, and c = 2. Just replace and calculate.
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x2+7x+12=0 x2+7x=-12 x+Sqaure Root of 7x= 2(SQ Root Symbol)3
x2 + 7x + 9 = 3 ∴ x2 + 7x + 6 = 0 ∴ (x + 6)(x + 1) = 0 ∴ x ∈ {-6, -1}
x2+7x+12
X^2 + 7X + 18 = 0 try the discriminant b^2 - 4ac 7^2 - 4(1)(18) 49 - 72 < 0 so, no real roots and no factors of 18 add to 7
No real roots