Question

Determine the nature of root of the following quadratic equation
(b + c) x² (a + b + c) x + a = 0​

Answer 1

Determine the nature of root of the following quadratic equation

(b + c) x² (a + b + c) x + a = 0

x²b+x²c(ax+bx+cx)+a

(Ax+bx+cx)²-4(x²b+x²c)+a=0

You can solve further after solving you can know

this equation that it is equal, real, rational , irrational.

please give me brainliest for my time

Answer 2

Step-by-step explanation:

In the equation,

(b + c) x² + (a + b + c) x + a = 0

Discriminant,

D = (a + b + c)² - 4×(b + c)×a

= a² + b² + c² + 2ab + 2bc + 2ca - 4ab - 4bc

= a² + b² + c² - 2ab - 2bc + 2ca

= (a - b + c)²

Here, D is a perfect square. So, D>=0

=> the roots are real

if D=0 => 2 real and equal roots

if D>0 => 2 real and different roots