Question

3) if the difference of the roots of x^2+2px+q=0 and x^2+2qx+p=0 is equal , then prove that p+q+1=0. ​

Answer 1

ANSWER

Let α and β are the roots of equation,

x

2

+2px+q=0\\ α−β=CAlso x

2

+qx+p=0

α

′

−β

′

=C

α−β=α

′

−β

′

(α+β)

2

−4αβ

=

(α

,

+β

,

)

2

−4α

′

β

′

(−2p)

2

−4q

=

(−2q)

2

−4p

4p

2

−4q

2

=4q−4p

p

2

−q

2

=q−p

(p−q)(p+q)=−(p−q)

p+q=−1

p+q+1=0