Question

The number of roots of the equation | x |2

– 5 | x | + 6 = 0 is​

Answer 1

Let ∣x∣=y

So given equation becomes, y^2 −5y+6=0

⇒(y−2)(y−3)=0, factor

we get,

⇒y=2,3  

⇒∣x∣=2,3, substitute back y=∣x∣

⇒x=±2,±3, modulus property  

Hence number of real roots are 4