Question

If all integers satisfying the inequality $\frac{(x-1{)}^2(x-2{)}^3(x-4{)}^5(x-5{)}^5}{(x-5{)}^2}\ge 0$ are arranged in increasing order then the quadratic equation with the first and fifth integers in the list as roots is -

• A. $x^2-8x+12=0$
• B. $x^2-9x+14=0$
• C. $x^2-5x+4=0$
• D. $x^2-7x+6=0$

Answer 1

The correct option is D $x^2-7x+6=0$

- . - . + . - . +
1 2 4 5

$\Rightarrow 2\le x\le 4$ or x > 5 or x = 1
So first integer = 1, fifth integer = 6
Hence, $x^2-7x+6=0$ is the required equation.