Question

If x is real, find the range of y from the equation $x^2(y-1)-2x+(2y-1)$ = 0

• A. $[0,2]$
• B. $[0,\frac{3}{2}]$
• C. $[0,\frac{7}{2}]$
• D. (-$\infty$, 0 ]

Answer 1

The correct option is B

$[0,\frac{3}{2}]$

If x is real,

D $\ge$ 0

$b^2-4ac\ge 0$

$4-4(y-1)(2y-1)\ge 0$

$1-(y-1)(2y-1)\ge 0$

(y - 1) (2y - 1) $\le$ 1

$2y^2-3y\le 0$

$y(2y-3)\le 0$

(y - 0)($y-\left(\frac{3}{2}\right))\le 0$

$0\le y\le$ $\frac{3}{2}$