State whether the quadratic equation $(x-1)(x+2)+2=0$ has two distinct real roots. Justify your answer.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Given equation is $(x-1)(x+2)+2=0$.
Expanding the terms,we get $x^{2} + 2x - x - 2 + 2 = 0$.
Simplifying,we get $x^{2} + x = 0$.
Comparing this with the standard form $ax^{2} + bx + c = 0$,we have $a = 1, b = 1, c = 0$.
The discriminant $D$ is given by $D = b^{2} - 4ac$.
Substituting the values,$D = (1)^{2} - 4(1)(0) = 1 - 0 = 1$.
Since $D > 0$,the quadratic equation has two distinct real roots.

Explore More

Similar Questions

Solve the following quadratic equation using the quadratic formula: $3x^{2} + 2\sqrt{5}x - 5 = 0$.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $x^{2}-5x-1=0$

Find the discriminant of the following quadratic equation: $5x^{2} + 2x - 1 = 0$.

Find the roots of the quadratic equation using the quadratic formula:
$2x^{2} - 3x - 5 = 0$

$(x^{2}+1)^{2}-x^{2}=0$ has

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo