Write the number of quadratic equation with real roots, which do not change by squaring their roots.

Answer

`x^{2}`,
`x^{2}-1`,
`x^{2}-2 x+1`
are 3 equations possible

Explanation

Let a and b be the real roots of the quadratic equation.

We need to find the number of quadratic equations such that they remain unchanged even if roots are squared.



`a^{2}=a and b^{2}=b`



`Rightarrow a^{2}-a=0 and b^{2}-b=0`

`Rightarrow {a}({a}-1)=0 and {b}({b}-1)=0`

`Rightarrow a=0 or a=1 and b=0 or b=1`

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