Question

Determine the nature of the roots of the following quadratic equations from their discriminant: 3y^2+9y+4=0​

Answer 1

Answer:

Step-by-step explanation:

Given equation is, 3y² +9y+4=0

We know,D=b ²−4ac

a=3,b=9,c=4

D=(9)²−4(3)(4)

∴D=33

Since, D>0 the roots are real and unequal.

Answer 2

Answer:

real and distinct and irrational.

Step-by-step explanation:

Comparing the given equation with $ax^{2}+bx+c=0$ ;

a = 3 ; b = 9 ; c = 4 ; x = y .

Therefore, discriminant , $D={b^{2}-4ac}$

                                              = 81-48 = 33>0.   (not a perfect square.)

Hence, the roots are real and distinct and irrational.