Quadratic Equations Part II

Algebra Level 4

$\sqrt {x-2}(x^{2} -4x +3) = 0$

What is the number of roots of the equation above?

Note: Treat the square root as a real valued function.

2 None of these choices 0 3

2 solutions

Shivam Jadhav
Apr 5, 2015

By seeing it we can say it has 3 roots but one of the root , which is 1 when put in $\sqrt{x-2}$ becomes non- real. Therefore the roots are 2 and 3.

yeah the equation has 3 roots because the equation turns out to be zero at x=1,x=2,x=3

Yash Singh - 6 years, 2 months ago

So what?? It becomes complex...A complex number multiplied by 0 is also 0...

A Former Brilliant Member - 6 years, 2 months ago

yes i have the same doubt...can anyone clear it

Harshi Singh - 5 years, 10 months ago

@Satvik Golechha @Tanishq Varshney ...Guys, help! Why can't we consider 1??

A Former Brilliant Member - 5 years, 10 months ago

@A Former Brilliant Member – I don't know whether the problem has been edited, but it says the square root yields a real valued function, so we have to find values of x>=2

Tanishq Varshney - 5 years, 10 months ago

@Tanishq Varshney – Cool, thanks:)

A Former Brilliant Member - 5 years, 10 months ago

Vasudev Chandna
Apr 6, 2015

Since the equation is given equal to zero, just remove root(x-2) by shifting it to RHS.

The number of roots of the quadratic equation thus left will be 2

You got the point of the most precise concept, while others are struggling with complex.

Muhammad Arifur Rahman - 6 years, 1 month ago

Quadratic Equations Part II

2 solutions

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