Question 5 - Case Based Questions (MCQ) - Chapter 2 Class 10 Polynomials (Term 1)

Last updated at Aug. 13, 2021 by

For a linear polynomial kx + c, k ≠ 0, the graph of y = kx + c is a straight line which intersects the X-axis at exactly one point, namely, ((-c)/k,0), Therefore, the linear polynomial kx + c, k ≠ 0, has exactly one zero, namely, the X-coordinate of the point where the graph of y = kx + c intersects the X-axis.

Question 1

If a linear polynomial is 2x + 3, then the zero of 2x + 3 is:

(a) 3/2

(b) − 3/2

(c) 2/3

(d) − 2/3

Question 2

The graph of y = p(x) is given in figure below for some polynomial p(x). The number of zero/zeroes of p(x) is/are:

(a) 1

(b) 2

(c) 3

(d) 0

Question 3

If 𝛼 and 𝛽 are the zeroes of the quadratic polynomial x
^{
2
}
– 5x + k such that 𝛼 – 𝛽 = 1, then the value of k is:

(a) 4

(b) 5

(c) 6

(d) 3

Question 4

If α and β are the zeroes of the quadratic polynomial p(x) = 4x2 + 5x + 1, then the product of zeroes is:

(a) −1

(b) 1/4

(c) −2

(d) − 5/4

Question 5

If the product of the zeroes of the quadratic polynomial p(x) = ax
^{
2
}
– 6x – 6 is 4, then the value of a is:

Question For a linear polynomial kx + c, k ≠ 0, the graph of y = kx + c is a straight line which intersects the X-axis at exactly one point, namely, ((−𝑐)/𝑘,0), Therefore, the linear polynomial kx + c, k ≠ 0, has exactly one zero, namely, the X-coordinate of the point where the graph of y = kx + c intersects the X-axis. Give answer the following questions:
Question 1 If a linear polynomial is 2x + 3, then the zero of 2x + 3 is: (a) 3/2 (b) − 3/2 (c) 2/3 (d) − 2/3
Let p(x) = 2x + 3
Finding zero
p(x) = 0
2x + 3 = 0
2x = – 3
x = (−𝟑)/𝟐
So, the correct answer is (B)
Question 2 The graph of y = p(x) is given in figure below for some polynomial p(x). The number of zero/zeroes of p(x) is/are: (a) 1 (b) 2 (c) 3 (d) 0
Number of zeroes is equal to number of times parabola intersects the x-axis
Since the graph does not intersect the X-axis,
∴ Number of zeroes = 0
So, the correct answer is (d)
Question 3 If 𝛼 and 𝛽 are the zeroes of the quadratic polynomial x2 – 5x + k such that 𝛼 – 𝛽 = 1, then the value of k is: (a) 4 (b) 5 (c) 6 (d) 3
Let p(x) = x2 – 5x + k
Now,
Sum of zeros = 𝒄/𝒂
𝛼 + 𝛽 = (−(−5))/1
𝛼 + 𝛽 = 5
Also given,
𝜶 − 𝜷 = 1
Product of zeros = 𝒄/𝒂
𝛼𝛽 = 𝑘/1
𝛼𝛽 = k
Adding (1) and (2)
𝛼 + 𝛽 + 𝛼 − 𝛽 = 5 + 1
2𝛼 = 6
𝛼 = 6/2
𝛼 = 3
Putting 𝛼 = 3 in (1)
𝛼 + 𝛽 = 5
3 + 𝛽 = 5
𝛽 = 5 − 3
𝛽 = 2
Now, from (3)
𝛼𝛽 = k
3 × 2 = k
6 = k
k = 6
So, the correct answer is (C)
Question 4 If 𝛼 and 𝛽 are the zeroes of the quadratic polynomial p(x) = 4x2 + 5x + 1, then the product of zeroes is: (a) −1 (b) 1/4 (c) −2 (d) − 5/4
Given
p(x) = 4x2 + 5x + 1
Now,
Product of Zeros = 𝑐/𝑎
= 𝟏/𝟒
So, the correct answer is (B)
Question 5 If the product of the zeroes of the quadratic polynomial p(x) = ax2 – 6x – 6 is 4, then the value of a is: (a) − 3/2 (b) 3/2 (c) 2/3 (d) − 2/3
Given
p(x) = ax2 – 6x – 6
Here,
Product of zeroes = 𝑐/𝑎
4 = (−𝟔)/𝒂
4a = −6
a = (−6)/4
a = (−𝟑)/𝟐
So, the correct answer is (A)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.