MEDIUM
JEE Main/Advance
IMPORTANT
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If a,b are non-zero real numbers and α,β are the roots of x2+ax+b=0, then

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Important Questions on Quadratic Equations

HARD
JEE Main/Advance
IMPORTANT
If α,β are the roots of ax2+bx+c=0 (a0) and α+δ,β+δ are the roots of Ax2+Bx+C=0 (A0) for some constant δ, then
MEDIUM
JEE Main/Advance
IMPORTANT
If one root of the equation 4x2+2x-1=0 is α'', then
HARD
JEE Main/Advance
IMPORTANT
If α, β are the roots of x2+3x+1=0, then
HARD
JEE Main/Advance
IMPORTANT
If both roots of x2-32x+c=0 are prime numbers, then possible values of c are
EASY
JEE Main/Advance
IMPORTANT
Let f(x)=x2-a(x+1)-b=0,a,bR-{0},a+b0. If α and β are roots of equation f(x)=0, then the value of 1α2-aα+1β2-aβ-2a+b is equal to
HARD
JEE Main/Advance
IMPORTANT
If f(x) is a polynomial of degree three with leading coefficient 1 such that f(1)=1, f(2)=4, f(3)=9, then
HARD
JEE Main/Advance
IMPORTANT
Let P(x)=x32-x25+x18-x11+x4-x3+1. Which of the following are CORRECT?
HARD
JEE Main/Advance
IMPORTANT
If α, β are the real and distinct roots of x2+px+q=0 and α4, β4 are the roots of x2-rx+s=0, then the equation x2-4qx+2q2-r=0 always has α-β