HARD
JEE Main/Advance
IMPORTANT
Earn 100

If α, β are the roots of the quadratic equation cx2-2bx+4a=0, then find the quadratic equation whose roots are 1+α1α, 1+β1β.

Important Questions on Quadratic Equations

HARD
JEE Main/Advance
IMPORTANT

If α, β are the roots of the quadratic equation cx2-2bx+4a=0, then find the quadratic equation whose roots are αβ, βα.

MEDIUM
JEE Main/Advance
IMPORTANT
If r be the ratio of the roots of the equation ax2+bx+c=0, show that r+12r=b2ac.
HARD
JEE Main/Advance
IMPORTANT
If 2p3-9pq+27r=0, then prove that the roots of the equations rx3-qx2+px-1=0 are in H.P..
MEDIUM
JEE Main/Advance
IMPORTANT
If α, β, γ are the roots of the equation x3+qx+r=0, then find the equation whose roots are 2α+2β+γ, α+2β+2γ, 2α+β+2γ.
HARD
JEE Main/Advance
IMPORTANT

If α, β, γ are the roots of the equation x3+qx+r=0, then find the equation whose roots are -rα, -rβ, -rγ.

HARD
JEE Main/Advance
IMPORTANT

If α, β, γ are the roots of the equation x3+qx+r=0, then find the equation whose roots are α+β2, β+γ2, γ+α2.

HARD
JEE Main/Advance
IMPORTANT

If α, β, γ are the roots of the equation x3+qx+r=0, then find the equation whose roots are -α3, -β3, -γ3.

HARD
JEE Main/Advance
IMPORTANT
Find the sum of all the values of k for which the expression 4-kx2+2k+2x+8k+1 will be a perfect square?