State whether the quadratic equation $(x-\sqrt{2})^{2}-2(x+1)=0$ 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 $(x-\sqrt{2})^{2}-2(x+1)=0$.
Expanding the equation: $x^{2}-2\sqrt{2}x+2-2x-2=0$.
Simplifying: $x^{2}-(2+2\sqrt{2})x=0$.
Comparing with $ax^{2}+bx+c=0$,we get $a=1, b=-(2+2\sqrt{2}), c=0$.
The discriminant $D = b^{2}-4ac = (-(2+2\sqrt{2}))^{2}-4(1)(0)$.
$D = (2+2\sqrt{2})^{2} = 4 + 8 + 8\sqrt{2} = 12+8\sqrt{2}$.
Since $D > 0$,the quadratic equation has two distinct real roots.

Explore More

Similar Questions

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

Which of the following polynomials does not have any real zero?

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}+5x+5=0$

If the value of the discriminant of a quadratic equation $6x^{2}-x-k=0$ is $25$,then $k = \ldots$

Values of $k$ for which the quadratic equation $2x^{2}-kx+k=0$ has equal roots is

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