Question

If the difference of the roots of the equation x²+px+q=0 be the same as that of the roots x²+qx+p=0, then prove that p+q+4=0;p≠q.​

Answer 1

Step-by-step explanation:

sum of roots of first equation is -p

product of roots of first equation is q

sum of roots of second equation is -q

product of roots of second equation is p

difference between two roots of first equation is √(p^2-4q)

difference between roots of second equation is√(q^2-4p)

given that difference between the roots of two equations are equal

√(p^2-4q)=√(q^2-4p)

p^2-4q=q^2-4p

p^2-q^2=-4p+4q

(p+q)(p-q)=-4(p-q)

p+q=-4

p+q+4=0