Question

Use the discriminant to determine the number and type of solutions for the following equation. 12x2 + 10x + 5 = 0

Answer 1

Zero real solutions I just did the test

Answer 2

Discriminant D is given by:
D=b²-4ac
Implication of discriminant is as follows:

D<0 two zeros that are complex conjugate
D=0 one real zero of multiplicity 2
D>0 two distinct real zers
D= (+ve perfet square)  two distinct rational zeros
From:
12x^2+10x+5=0
plugging in the equation we get:
10²-4×12×5
=100-240
=-140
thus
D<0

Answer is: 
A two irrational solutions