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Pair of Liner Equation in Two Variable

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(A) a unique solution (B) exactly two solutions
(C) infinitely many solutions (D) no solution

Pair of Liner Equation in Two Variable

The sum of the digits of a two-digit number is 9. If 27 is addedto it, the digits of the number get reversed. The number is 
(A) 25 (B) 72 (C) 63 (D) 36

Pair of Liner Equation in Two Variable

The pair of equations 5x – 15y = 8 and 3x – 9y =24/5 has 

(A) one solution (B) two solutions (C) infinitely many solutions (D) no solution

Polynomials

For which values of a and b, are the zeroes of q(x) = x³ + 2x² + a also the zeroes of the polynomial p(x) = x⁵ – x⁴ – 4x³ + 3x² + 3x + b? Which zeroes of  p(x) are not the zeroes of q(x)?

Polynomials

Find k so that x² + 2x + k is a factor of 2x⁴  + x³ – 14x² + 5x + 6. Also find all the zeroes of the two polynomials.

Polynomials

Given that the zeroes of the cubic polynomial x³ – 6x² + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Polynomials

If the remainder on division of x³ + 2x² + kx +3 by x – 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomial x³ + 2x² + kx – 18.

Polynomials

Find the zeroes of the polynomial x² + 1/6x – 2, and verify the relation between the coefficients and the zeroes of the polynomial. 

Polynomials

Are the following statement ‘True’ or ‘False’? Justify your answer.The only value of k for which the quadratic polynomial kx² + x + k has  equal zeros is  1/2

Polynomials

Are the following statement ‘True’ or ‘False’? Justify your answer.

If all three zeroes of a cubic polynomial x³ + ax² – bx + c are positive, then at least one of a, b and c is non-negative.