The condition that the product of two of...

The condition that the product of two of the roots of `x^(3)+px^(2)+qx+r`=0 may be -1 is
r(p+r)+q+1=0
q(p+q)+r+1=0
p(p+r)+q+1=0
p(p+q)+r+1=0

Similar Questions

Explore conceptually related problems

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in h.P is 2q^3=r (3 pq -r)

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P then 2q^3 =9r (pq-3r)

If p != 0, q != 0 and the roots of x^(2) + px +q = 0 are p and q, then (p, q) =

If all the roots of x^3 + px + q = 0 p,q in R,q != 0 are real, then

For p, q in R , the roots of (p^(2) + 2)x^(2) + 2x(p +q) - 2 = 0 are

find the condition that px^(3) + qx^(2) +rx +s=0 has exactly one real roots, where p ,q ,r,s,in R

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

Show that the reflection of the line px+qy+r=0 in the line x+y+1 =0 is the line qx+py+(p+q-r)=0, where p!= -q .

If alpha , beta , gamma are the roots of x^3 -px^2 +qx -r=0 and r ne 0 then find (1)/( alpha^2) +(1)/( beta^2) +(1)/( gamma ^2) in terms of p,q ,r