Question

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

solve this quadratic equation and tell if this has 2 distinct and real roots.​

Answer 1

Answer:

$= x ^{2} + 3x + 2 = 0$

$= x ^{2} + 2x + 1x + 2 = 0$

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

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

$x = - 1 \: or \: x = - 2$

Answer 2

(x) Given, (x + 1) (x – 2) + x = 0

Simplifying above equation we have:

⟹ x2 + x – 2x – 2 + x = 0

⟹ x2 – 2 = 0

⟹ x2 + 0 x – 2 = 0

On comparing with ax2 + bx + c = 0, we have

a = 1, b = 0 and c = –2

Now, D = b2 –4ac = (0)2 – 4(1) (–2) = 0 + 8 = 8 > 0

Hence, the equation (x + 1) (x – 2) + x = 0 has two distinct real roots.