1. Tardigrade
  2. Question
  3. Mathematics
  4. If the equations x2 + a x + 1 = 0 and x2 - x - a = 0 have a real common root b, then the value of b is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If the equations $x^2 + a x + 1 = 0$ and $x^2 - x - a = 0$ have a real common root b, then the value of b is equal to

KEAMKEAM 2018

Solution:

Given equations,
$x^{2}+a x+1=0$
$x^{2}-x-a=0$
$\because b$ is common root, so $b$ satisfied both equations.
$b^{2}+ a b +1 =b^{2}-b-a$
$= a b +b =-a-1$
$\Rightarrow b(a+1) = -(a+1)$
$\Rightarrow b = -1$