If the equations x2 + bx - 1 = 0 and x2 + x + b = 0 have a common root different from -1, then |b| is equal to :

Question

If the equations x2 + bx - 1 = 0 and x2 + x + b = 0 have a common root different from -1, then |b| is equal to : (A) √2 (B) 2 (C) 3 (D) √3

Tardigrade Admin · Accepted Answer

x2+bx-1=0 common root x2+x+b=0 (---/x=(b+1)b-1) Put x=(b+1/b-1)in equation (2) ((b+1/b-1))2+((b+1/b-1))+b=0 (b+1)2(b+1)(b-1)+b(b-1)2=0 b2+1+2b+b2-1+b(b2-2b+1)=0 2b2+2b+b3-2b2+b=0 b3+3b=0 b(b2+3)=0 b2=-3 b=±√3i |b|=√3

Q. If the equations $x^{2} + b x - 1 = 0$ and $x^{2} + x + b = 0$ have a common root different from $- 1$ , then $∣ b ∣$ is equal to :

$2$

$2$

$3$

$3$

Q. If the equations x2+bx−1=0 and x2+x+b=0 have a common root different from −1, then ∣b∣ is equal to :

2​

2

3

3​

x2+bx−1=0 common root x2+x+b=0 x=b−1b+1​−−−​ Put x=b−1b+1​______in equation (2) (b−1b+1​)2+(b−1b+1​)+b=0 (b+1)2(b+1)(b−1)+b(b−1)2=0 b2+1+2b+b2−1+b(b2−2b+1)=0 2b2+2b+b3−2b2+b=0<br/>b3+3b=0 b(b2+3)=0 b2=−3 b=±3​i ∣b∣=3​

Q. If the equations $x^{2} + b x - 1 = 0$ and $x^{2} + x + b = 0$ have a common root different from $- 1$ , then $∣ b ∣$ is equal to :

$2$

$2$

$3$

$3$