CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics

SECTION C

Questions number 16 to 25 carry 3 marks each.

Q. 16. Prove that is an irrational number.

Sol. See Q. 16, 2009 (II Delhi). [Page 325 / 2007.

Q. 17. Find all other zeroes of x⁴ + x³– 23x² – 3x + 60, if it is given that two of its zeroes are and – .

Sol. Since two zeroes are and – . (x – ) (x + ) = x² – 3 is a factor of given polynomial.
x⁴ + x³–23x²– 3x + 60
= (x² – 3) (x² + x – 20)
= (x² – 3) (x² + 5x – 4x – 20)
= (x² – 3) [x(x + 5) – 4(x + 5)]
= (x + 3 )(x – 3 )(x – 4)(x + 5)
All other zeroes are x – 4 = 0 or x + 5 = 0
x = 4 or x = – 5

Q. 18. Check graphically whether the pair of equations 3x – 2y + 2 = 0 and x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the y-axis.

Sol. 3x – 2y + 2 = 0       x – y + 3 = 0

3x + 2 = 2y                x + 3 = y

By plotting the points and joining them, the lines donot intersect anywhere, i.e., they are parallel.
Given pair of equations is not consistent, i.e., inconsistent.
The equation 3x – 2y + 2 = 0 meets the y-axis at A(0, 1)
The equation x – y + 3 = 0 meets the y-axis at B(0, 3).

Mathematics 2009 Question Papers Class X
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