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NCERT Solutions · Maths Ch 2
Polynomials
18 questions · 2 exercises
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Ex 2.1
Ex 2.2
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
6 QUESTIONS
Exercise 2.1
Q1(i)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a straight line parallel to the x-axis, lying above it. It never touches the x-axis.
(1 mark)
Q1(ii)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a curve that dips below the x-axis and then rises steeply, crossing the x-axis once, to the right of O.
(1 mark)
Q1(iii)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a wave-like curve that rises, falls and rises again, crossing the x-axis at three points.
(1 mark)
Q1(iv)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a U-shaped (upward-opening) curve to the left of the y-axis, crossing the x-axis at two points.
(1 mark)
Q1(v)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a curve that goes up and down like a wave, crossing the x-axis at four points.
(1 mark)
Q1(vi)
The graphs of y = p(x) are given in Fig. 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in the following case.
Figure: a curve shaped like a wavy 'M', which crosses the x-axis at two points and touches it at a third point.
(1 mark)
2
12 QUESTIONS
Exercise 2.2
Q1(i)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: x² – 2x – 8
(3 marks)
Q1(ii)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: 4s² – 4s + 1
(3 marks)
Q1(iii)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: 6x² – 3 – 7x
(3 marks)
Q1(iv)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: 4u² + 8u
(3 marks)
Q1(v)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: t² – 15
(3 marks)
Q1(vi)
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: 3x² – x – 4
(3 marks)
Q2(i)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: 1/4, −1
(2 marks)
Q2(ii)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: √2, 1/3
(2 marks)
Q2(iii)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: 0, √5
(2 marks)
Q2(iv)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: 1, 1
(2 marks)
Q2(v)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: −1/4, 1/4
(2 marks)
Q2(vi)
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: 4, 1
(2 marks)