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Consider the following two statements
I. Any pair of consistent liner equations in two variables must have a unique solution.
II. There do not exist two consecutive integers, the sum of whose squares is 365 .

Then

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Important Questions on Polynomials

EASY

If one of the zeroes of the quadratic polynomial x2+3x+k is 2, then find the value of k is

EASY
Let fx be a polynomial with integer coefficients satisfying f1=5 and f2=7. The smallest possible positive value of f12 is
MEDIUM
The number of polynomials having zeroes 2 and 1 is 
MEDIUM
The number of polynomials p(x) with integer coefficients such that curve y=p(x) passes through (2,2) and (4,5) is
EASY
The common root of the equations x2-bx+c=0 and x2+bx-a=0 is
EASY
If 2x2+y2+8z2-22xy+42yz-8zx=Ax+y+Bz2, then the value of A2+B2-AB is:
EASY

The sum of the zeroes of the polynomial px=5x2+2x-3 is

EASY
The value of 27a3-22b3 is equal to:
MEDIUM
If 30x2-15x+1=0, then what is the value of 25x2+36x2-1?
EASY
The zeroes of the polynomial Px=x2-3x-4  will be : 
HARD
The remainder when the polynomial 1+x2+x4+x6+.....+x22 is divided by 1+x+x2+x3+.....+x11 is
EASY
The product of the zeros of 4u2+8u is
EASY
The quadratic polynomial the sum of whose zeros is -5 and their product is 6, is
EASY
The product of the zeroes of 3x2+11x-2 is: 
EASY

The zeros of a quadratic polynomial _____ are 4 and 3.

EASY

If α, β and γ are the zeros of a cubic polynomial px=ax3+bx2+cx+d, a0 then 1α+1β+1γ= _____.

EASY
If 1-64x3-12x+px2=1-4x3, then the value of p is:
HARD
Let t  be real number such that t2=at+b for some positive integers a and b. Then for any choice of positive integers a and b, t3 is never equal to
HARD
Number of integers k for which the equation x3-27x+k=0 has at least two distinct integer roots is