HARD
JEE Main
IMPORTANT
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If 2+3i is one of the roots of the equation 2x3-9x2+kx-13=0, kR, then the real root of this equation (where i2=-1) :

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Important Questions on Quadratic Equations

HARD
JEE Main
IMPORTANT
Let α and β be the roots of equation x2-6x-2=0. If an=αn-βn,  n1, then the value of a10-2a82a9 is equal to
HARD
JEE Main
IMPORTANT
If the two roots of the equation, a-1 x4+x2+1+a+1x2+x+12=0 are real and distinct, then the set of all values of a is equal to
MEDIUM
JEE Main
IMPORTANT
The equation 3x2+x+5=x-3, where x  is real, has
MEDIUM
JEE Main
IMPORTANT
If 1α,1β  are the roots of the equation ax2+bx+1=0, a0, a,bR, then the equation xx+b3+a3-3abx=0 has roots:
EASY
JEE Main
IMPORTANT
If equations ax2+bx+c=0, a, b, cR, a0 and 2x2+3x+4=0  have a common root, then a:b:c equals :
HARD
JEE Main
IMPORTANT
Let α  and  β be the roots of equation px2+qx+r = 0, p0. If p, q, r are in A.P. and 1 α + 1 β = 4 , then the value of α - β is 
HARD
JEE Main
IMPORTANT
The real number k for which the equation, 2x3+3x+k=0 has two distinct real roots in [0, 1] belongs to
EASY
JEE Main
IMPORTANT
If the equations x 2 + 2 x + 3 = 0 and a x 2 +bx+c=0, a,b,cR, have a common root, then a:b:c is: