List of top Quantitative Aptitude Questions on Common Roots asked in CAT

If \((3+2\sqrt2)\) is a root of the equation ax2 + bx + c = 0 and \((4+2\sqrt3)\) is a root of the equation ay² + my + n = 0,where a,b,c,m and n are integers, then the value of \((\frac{b}{m}+\frac{c−2b}{n})\) is

Let r and c be real numbers. If r and −r are roots of 5x3+cx2−10x+9=0,then c equals

Suppose k is any integer such that the equation \(2x^2+kx+5=0\) has no real roots and the equation \(x^2+(k−5)x+1=0\) has two distinct real roots for x. Then, the number of possible values of k is

What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?