Polynomials-linear equation test paper

10TH Mathematics
Section A
Solve any five of the following 5x3=15
1. Find the value of a and b for which the following system of linear equations has infinite numbers of solutions:
2x - 3y = 7 (a + b) x - (a + b - 3)y = 4a + b.) Solve the following system of linear equations

2. For what value of k will the system of equations

x + 2y = 5; 3x + ky + 15 = 0 has (i) unique solution (ii) no solution

3. solve the following system of linear equations: ax + by = c, b x + ay = 1 + c 4

4. Find a quadratic polynomial whose the sum and product of its zeros respectively. √3,2

5. If a and b are the zeros of a given quadratic polynomial f(x) = x2 + x - 2, find the value of 1/a + 1/b

6. If 2, ½ are the zeros of px2+5x+r, prove that p= r.

Section B       Solve any five questions 5x4=20

1. Find the zeros of the quadratic polynomial x2+ 9x + 20 , and verify the basic relationships between the zeros and the coefficients.

2. Five years ago, Neeta was trice as old as Reeta. Ten years later, Neeta will be twice as old as Reeta, How old are Neeta and Reeta now?

3. Person can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man’s speed of rowing is still water and the speed of the current.

4. The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

5. There are two class rooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 student are shifted from room B to room A, the resulting number of student's in room A becomes double the number of student left in room B. find the original number of student in the two rooms separately.

6. Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time . If they moves in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hours and 20 minutes. Find the speed of the cars.

7. If a & ß are the zeroes of the polynomial 2x2 _ 4x + 5, then find the value of a3 + ß3