Q the value of 'b' for which equations x2+bx-1=0 x2+x+b=0 have one root in common is - Maths - Complex Numbers and Quadratic Equations

Question

Q the value of 'b' for which
equations
x2+bx-1=0
x2+x+b=0
have one root in common is ??

Priyanka Kedia · Accepted Answer

The given equation be as,x2+bx-1=0 1x2+x+b=0 2Let α be the
common root So, α satisfies both the equations
α2+bα-1=0 3α2+α+b=0 4Subtracting equation 3 and
4, we have,αb-1-1-b=0⇒α=1+bb-1Substitute value of
α in equation3, we have,
1+bb-12+b1+bb-1-1=0⇒1+b2+bb2-1-b-12=0⇒
b3+3b=0⇒bb2+3=0⇒b=0,±3i

Q . the value of 'b' for which equations x2+bx-1=0 x2+x+b=0 have one root in common is ??

Q . the value of 'b' for which equations

x²+bx-1=0

x²+x+b=0

have one root in common is ??