Quadratic equations

Question

b² – 4ac part of the quadratic formula is called “discriminant” and can be used to determine the number and type of solution(s). Determine the number and type of solution(s) of the following equations.(a) 3x² + 7x + 2 = 0                       (b) 4x² + 12x + 9 = 0

Is there a way to memorize the quadratic formula beyond just repeating it? What would be a creative way for someone to learn this formula?

Answer 1

(a) 3x² + 7x + 2 = 0  

(3x+1)(x+2)=0

x=-1/3 and -2

 (b) 4x² + 12x + 9 = 0

(2x+3)(2x+3)

x=-1.5

Answer 2

Hi, Myrka

All quadratic equations have two solutions.

If b²-4ac>0 then there are two real and distinct zeros (two solutions both of multiplicity one).

If b²-4ac=0 then there is one real and repeated zero (one solution of multiplicity two).

If b²-4ac<0 then there are two complex conjugate zeros (two complex solutions both of multiplicity one).

Best,

Tomás