Polynomials
Previous Year Solved Questions 2021
1. If one of the zeroes of a quadratic polynomial (k-1)x² + kx + 1 is -3, then the value of k is: [Term I, 2021-2022]
(a) 4/3 (b) -4/3 (c) 2/3 (d) -2/3
(a) 4/3 (b) -4/3 (c) 2/3 (d) -2/3
View Answer
Ans: (a) 4/3
Since -3 is a zero:
(k-1)(-3)² + k(-3) + 1 = 0
9(k-1) – 3k + 1 = 0
9k – 9 – 3k + 1 = 0
6k – 8 = 0
k = 8/6 = 4/3
Since -3 is a zero:
(k-1)(-3)² + k(-3) + 1 = 0
9(k-1) – 3k + 1 = 0
9k – 9 – 3k + 1 = 0
6k – 8 = 0
k = 8/6 = 4/3
Case Study: A car moves on a highway. The path it traces is given below:
Based on the above information, attempt any 4 questions:
1. What is the shape of the curve EFG? [Term I, 2021-22]
(a) Parabola (b) Ellipse (c) Straight line (d) Circle
(a) Parabola (b) Ellipse (c) Straight line (d) Circle
View Answer
Ans: (a) Parabola
The curve EFG shows a U-shaped graph, characteristic of a quadratic polynomial/parabola.
The curve EFG shows a U-shaped graph, characteristic of a quadratic polynomial/parabola.
2. If the curve ABC is represented by polynomial -(x²+4x+3), then its zeroes are: [Term I, 2021-22]
(a) 1 and -3 (b) -1 and 3 (c) 1 and 3 (d) -1 and -3
(a) 1 and -3 (b) -1 and 3 (c) 1 and 3 (d) -1 and -3
View Answer
Ans: (d) -1 and -3
-(x²+4x+3) = -x² – 4x – 3 = 0
Multiply by -1: x² + 4x + 3 = 0
Factor: (x+1)(x+3) = 0
Zeroes: x = -1, -3
-(x²+4x+3) = -x² – 4x – 3 = 0
Multiply by -1: x² + 4x + 3 = 0
Factor: (x+1)(x+3) = 0
Zeroes: x = -1, -3
3. If the path traced by the car has zeroes at -1 and 2, then it is given by: [Term I, 2021-22]
(a) x²+x+2 (b) x²-x+2 (c) x²-x-2 (d) x²+x-2
(a) x²+x+2 (b) x²-x+2 (c) x²-x-2 (d) x²+x-2
View Answer
Ans: (c) x²-x-2
Zeroes: -1 and 2
Sum = -1+2 = 1
Product = (-1)×2 = -2
Polynomial: x² – (1)x + (-2) = x² – x – 2
Zeroes: -1 and 2
Sum = -1+2 = 1
Product = (-1)×2 = -2
Polynomial: x² – (1)x + (-2) = x² – x – 2
4. The number of zeroes of the polynomial representing the whole curve is: [Term I, 2021-22]
(a) 4 (b) 3 (c) 2 (d) 1
(a) 4 (b) 3 (c) 2 (d) 1
View Answer
Ans: (a) 4
Graph intersects x-axis at 4 points: x = -3, -1, 2, 5
So 4 zeroes.
Graph intersects x-axis at 4 points: x = -3, -1, 2, 5
So 4 zeroes.
5. The distance between C and G is: [Term I, 2021-22]
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
View Answer
Ans: (b) 6 units
From graph: C at x=8, G at x=2
Distance = |8-2| = 6 units
From graph: C at x=8, G at x=2
Distance = |8-2| = 6 units
Q6: If one zero of the quadratic polynomial x² + 3x + k is 2, then find the value of k. [CBSE 2021]
View Answer
Ans: k = -10
Since 2 is a zero:
f(2) = 2² + 3×2 + k = 0
4 + 6 + k = 0
10 + k = 0
k = -10
Since 2 is a zero:
f(2) = 2² + 3×2 + k = 0
4 + 6 + k = 0
10 + k = 0
k = -10