Question

Suppose that two persons $A$ and $B$ solve the equation $ {{x}^{2}}+ax+b=0 $ . While solving $A$ commits a mistake in the coefficient of $ x $ was taken as $15$ in place of $-9$ and finds the roots as $ -7 $ and $ -2 $ . Then, the equation is

• A. $ {{x}^{2}}+9x+14=0 $
• B. $ {{x}^{2}}-9x+14=0 $
• C. $ {{x}^{2}}+9x-14=0 $
• D. $ {{x}^{2}}-9x-14=0 $

Answer 1

The Correct Option is B

Let the incorrect equation is $ {{x}^{2}}+15x+b=0 $ .
Since, roots are $ -7 $ and $ -2 $ .
$ \therefore $ Product of roots, $ b=14 $
So, correct equation is $ {{x}^{2}}-9x+14=0 $