Polynomials
Previous Year Solved Questions 2022
1: If one of the zeroes of a quadratic polynomial (k-1)x² + kx + 1 is -3, then the value of k is. [CBSE 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
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Ans: (a) 4/3
Since -3 is a zero:
(k-1)(-3)² + k(-3) + 1 = 0
(k-1)(9) – 3k + 1 = 0
9k – 9 – 3k + 1 = 0
6k – 8 = 0
6k = 8
k = 8/6 = 4/3
Since -3 is a zero:
(k-1)(-3)² + k(-3) + 1 = 0
(k-1)(9) – 3k + 1 = 0
9k – 9 – 3k + 1 = 0
6k – 8 = 0
6k = 8
k = 8/6 = 4/3
2: If the path traced by the car has zeroes at -1 and 2, then it is given by [CBSE 2022]
(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
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Ans: (c) x² – x – 2
Zeroes: -1 and 2
Sum = -1 + 2 = 1
Product = (-1)×2 = -2
Polynomial: x² – (sum)x + (product)
= x² – 1x + (-2)
= x² – x – 2
Zeroes: -1 and 2
Sum = -1 + 2 = 1
Product = (-1)×2 = -2
Polynomial: x² – (sum)x + (product)
= x² – 1x + (-2)
= x² – x – 2
3: The number of zeroes of the polynomial representing the whole curve is [CBSE 2022]
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
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Ans: (a) 4
Number of zeroes = Number of times graph intersects x-axis.
From graph: 4 intersection points.
Number of zeroes = Number of times graph intersects x-axis.
From graph: 4 intersection points.
Q4: The distance between C and G is [CBSE 2022]
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
(a) 4 units (b) 6 units (c) 8 units (d) 7 units
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Ans: (b) 6 units
C at position 2, G at position 8
Distance = |8 – 2| = 6 units
C at position 2, G at position 8
Distance = |8 – 2| = 6 units
Q5: The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6. [CBSE 2022]
(a) x² + 5x + 6 (b) x² – 5x + 6 (c) x² – 5x – 6 (d) -x² + 5x + 6
(a) x² + 5x + 6 (b) x² – 5x + 6 (c) x² – 5x – 6 (d) -x² + 5x + 6
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Ans: (a) x² + 5x + 6
Sum = -5, Product = 6
Polynomial: x² – (sum)x + (product)
= x² – (-5)x + 6
= x² + 5x + 6
Sum = -5, Product = 6
Polynomial: x² – (sum)x + (product)
= x² – (-5)x + 6
= x² + 5x + 6