Question

The roots of the equation (x+10)(x+1)+19 is given by a and b. The greater ratio of roots of (x+a)(x+b)-11 is ___. (The answer will be of p/q form where p and q are integers, then input 'pq' in the provided space.)

Answer 1

(x+10)(x+1)+19 = $x^2+11x+29$
Since a and b are the roots, a+b= -11 and ab=29
$\therefore$ (x+a)(x+b)-11 =
$x^2+(a+b)x+ab-11$
=$x^2-11x+18$
=(x-9)(x-2)
ie., the roots are 9 and 2.
$Thegreaterratiois\frac{9}{2}$.