NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 2: PolynomialsExercise 2.1
Class 10 - Mathematics - CHAPTER 2: Polynomials
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Question. 1
If one of the zeroes of the quadratic polynomial \((k-1)x^2 + kx + 1\) is \(-3\), then the value of k is
\(\dfrac{4}{3}\)
\(-\dfrac{4}{3}\)
\(\dfrac{2}{3}\)
\(-\dfrac{2}{3}\)
Question. 2
A quadratic polynomial, whose zeroes are \(-3\) and \(4\), is
\(x^2 - x + 12\)
\(x^2 + x + 12\)
\(\dfrac{x^2}{2} - \dfrac{x}{2} - 6\)
\(2x^2 + 2x - 24\)
Question. 3
If the zeroes of the quadratic polynomial \(x^2 + (a+1)x + b\) are \(2\) and \(-3\), then
\(a = -7,\; b = -1\)
\(a = 5,\; b = -1\)
\(a = 2,\; b = -6\)
\(a = 0,\; b = -6\)
Question. 4
The number of polynomials having zeroes as \(-2\) and \(5\) is
1
2
3
more than 3
Question. 5
Given that one of the zeroes of the cubic polynomial \(ax^3+bx^2+cx+d\) is zero, the product of the other two zeroes is
\(-\dfrac{c}{a}\)
\(\dfrac{c}{a}\)
0
\(-\dfrac{b}{a}\)
Question. 6
If one of the zeroes of the cubic polynomial \(x^3+ax^2+bx+c\) is \(-1\), then the product of the other two zeroes is
\(b-a+1\)
\(b-a-1\)
\(a-b+1\)
\(a-b-1\)
Question. 7
The zeroes of the quadratic polynomial \(x^2 + 99x + 127\) are
both positive
both negative
one positive and one negative
both equal
Question. 8
The zeroes of the quadratic polynomial \(x^2 + kx + k\), where \(k \ne 0\), are:
cannot both be positive
cannot both be negative
are always unequal
are always equal
Question. 9
If the zeroes of the quadratic polynomial \(ax^2 + bx + c\), with \(c \ne 0\), are equal, then
\(c\) and \(a\) have opposite signs
\(c\) and \(b\) have opposite signs
\(c\) and \(a\) have the same sign
\(c\) and \(b\) have the same sign
Question. 10
If one of the zeroes of a quadratic polynomial of the form \(x^2+ax+b\) is the negative of the other, then it
has no linear term and the constant term is negative
has no linear term and the constant term is positive
can have a linear term but the constant term is negative
can have a linear term but the constant term is positive
Question. 11
Which of the following is not the graph of a quadratic polynomial?
