Question

The equation $|1-x|+x^2=5$ has

• A. A rational root and an irrational root
• B. Two rational
• C. Two irrational roots
• D. No real roots

Answer 1

The correct option is A A rational root and an irrational root

$|1-x|+x^2=5$

$\Rightarrow |1-x|=5-x^2$

There are two cases possible

$(1-x)=5-x^2$ or $1-x=-5+x^2$

$\Rightarrow x^2-x-4=0$ or $x^2+x-6=0$

$x=\frac{1\pm \sqrt{17}}{2}$ or $x=\frac{-1\pm \sqrt{25}}{2}$

$x=\frac{1\pm \sqrt{17}}{2}$ or $x=-3,2$

Two irrational roots.