Question

Characterize the roots of the following quadratic using the discriminant 2x^2 + 6x + 3 = 0

Answer 1

Answer :

Real and unequal roots

Step-by-step explanation :

Given quadratic equation,

2x² + 6x + 3 = 0

It is of the form ax² + bx + c = 0

a = 2, b = 6, c = 3

$\boxed{Discriminant, D=b^2-4ac}$

$D=6^2-4(2)(3) \\ D=36-24\\D=12 \\\\ => D>0 \\\\ \text{It has real and unequal roots}$

NATURE OF ROOTS :

If D < 0 ; no real roots

If D = 0 ; real and equal roots

If D > 0 ; real and unequal roots