Question

If m and n are the zeros of x^2-p(x+1)-c find (m+1)(n+1)

Answer 1

Answer:

If m and n are the roots of the equation (x+p)(x+q)−k=0, then the roots of the equation (x−m)(x−n)+k=0 are-

A .

p and q

B .

1/p and 1/q

C .

−p and −q

D .

p+q and p−q

ANSWER

(x+p)(x+q)−k=0⟹x2+(p+q)x+pq−k=0

m and n are the roots of this equation

So, we have

Sum of roots =−(p+q)=m+n

Product of the roots =pq−k=mn

⇒pq=mn+k

Consider, (x−m)(x−n)+k=0 

⇒x2−(m+n)x+mn+k=0

Sum of roots is m+n

But m+n=(−p)+(−q)

Product of the roots =mn+k

But mn+k=pq=(−p)(−q)

Hence, the roots of the new equation are −p,−q