2014 · Q15
If m and n are the roots of the equation ax^2 + bx + c = 0, then the equation whose roots are (m^2 + 1)/m and (n^2 + 1)/n is
Elementary MathematicsAlgebra
- Aacx^2 + (ab + bc)x + b^2 + (a - c)^2 = 0
- Bacx^2 + (ab - bc)x + b^2 + (a - c)^2 = 0
- Cacx^2 + (ab - bc)x + b^2 - (a - c)^2 = 0
- Dacx^2 + (ab + bc)x + b^2 - (a - c)^2 = 0
Explanation
Sum and product of the new roots (m + 1/m), (n + 1/n) simplify using m+n = -b/a, mn = c/a to give option (a).