JEE Main || Algebra || Super Quiz 1

The sum of all real values of satisfying the equation is:

If the two roots of the equation, (a-1)(x⁴+x²+1)+(a+1)(x²+x+1)²=0 are real and distinct, then the set of all values of ‘a’ is:

If a ∈ R and the equation – 3(x – [x])² + 2(x – [x]) + a² = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

The number of values of k, for which the system of equations
(k + 1)x + 8y = 4k
kx + (k + 3)y = 3k − 1
has no solution, is

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x−1 and it leaves remainder 6 when divided by x+1; then:

If x is a solution of the equation,
then is equal to:

If λ ∈ R is such that the sum of the cubes of the roots of the equation, x² + (2 - λ)x + (10 - λ) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

If and are roots of the equation,  for some , and then is equal to :

Let α and β be the roots of equation px² + qx + r = 0, for p≠0. If p, q, r are in A.P. and (1/α)+(1/β) =4, then the value of
|α-β|is