Question

Solve x^2 + 5x - 14 = 0

Answer 1

x²+5x-14=0

per factorization

x²+7x-2x+14=0

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

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

x+7=0⇔x=-7

x-2=0⇔x=2

or with the discriminant

b²-4ac =5²-4(1*-14)=81

Δ=81

Δ is strictly positive, the equation x²+5x−14=0 admits two solutions

(-b-√Δ)/2a = (-5-9)/2 = 14/2=-7

(-b+√Δ)/2a =(-5+9)/2 =4/2 = 2

S{-7,2}