Question

State the nature of the given quadratic equation $(x+1)(x+2)+x=0$

• A. Real and Distinct Roots
• B. Real and Equal Roots
• C. Imaginary Roots
• D. None of the Above

Answer 1

Answer: (A)

Real and Distinct Roots

Expanding,
$(x+1)(x+2)+x=0$
$x^2+2x+x+2+x=0$
$x^2+4x+2=0$
$D=4^2-\left(4\right)\left(1\right)\left(2\right)$
$=16-8$
$=8$
$D>0$, therefore the given equation has two distinct real roots.