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Polynomials

10th Class - CBSE - Mathematics - 1338 Questions - 0 Concepts

Important Questions

Q1 Single Correct Medium
Let $$p(x) = ax^2 + bx + c$$ be a quadratic polynomial. It can have at most
  • A. One zero
  • B. Three zeros
  • C. None of these
  • D. Two zeros

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q2 Single Correct Medium
If the zeros of the quadratic polynomial $$ax^2+bx+c, c\neq 0$$ are equal, then
  • A. $$c$$ and $$a$$ have opposite signs
  • B. $$c$$ and $$b$$ have opposite signs
  • C. $$c$$ and $$b$$ have the same sign
  • D. $$c$$ and $$a$$ have the same sign

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q3 Single Correct Medium
If $$\alpha$$ and $$\beta$$ are the zeros of the polynomial $$f(x)=16x^2+4x-5$$ then $$\dfrac {1}{\alpha}+\dfrac {1}{\beta}$$ is equal to
  • A. $$\dfrac {2}{5}$$
  • B. $$\dfrac {5}{2}$$
  • C. $$\dfrac {3}{5}$$
  • D. $$\dfrac {4}{5}$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q4 Single Correct Medium
If $$\alpha, \beta$$ are the zeros of $$f(x)=2x^2+6x-6$$, then
  • A. $$\alpha+\beta > \alpha \beta$$
  • B. $$\alpha+\beta < \alpha \beta$$
  • C. $$\alpha+\beta+\alpha \beta$$
  • D. $$\alpha+\beta=\alpha \beta$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q5 Single Correct Medium
If $$\alpha, \beta, \gamma$$ are zeros of $$ax^3+bx^2+cx+d$$, then $$\alpha \beta \gamma =$$:
  • A. $$\dfrac {d}{a}$$
  • B. $$\dfrac {c}{a}$$
  • C. $$\dfrac {-c}{a}$$
  • D. $$\dfrac {-d}{a}$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q6 Single Correct Medium
If $$\alpha$$ and $$\beta$$ are the zeros of the polynomial $$f(x)=15x^2-5x+6$$ then $$\left (1+\dfrac {1}{\alpha}\right )\left (1+\dfrac {1}{\beta}\right )$$ is equal to
  • A. $$\dfrac {13}{2}$$
  • B. $$\dfrac {16}{3}$$
  • C. $$\dfrac {15}{2}$$
  • D. $$\dfrac {13}{3}$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q7 Single Correct Medium
If one of the zeros of a quadratic polynomial of the form $$x^2 + ax + b$$ is the negative of the other, then it
  • A. has no linear term and the constant term is positive
  • B. can have a linear term but the constant term is negative
  • C. can have a linear term but the constant term is positive
  • D. has no linear term and the constant term is negative

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q8 Single Correct Medium
If $$\alpha$$ and $$\beta$$ are the zeros of the polynomial $$f(x)=6x^2-3-7x$$, then $$(\alpha+1)(\beta+1)$$ is equal to
  • A. $$\dfrac {5}{2}$$
  • B. $$\dfrac {2}{5}$$
  • C. $$\dfrac {3}{5}$$
  • D. $$\dfrac {5}{3}$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q9 Single Correct Medium
If 2 and $$-\dfrac {1}{2}$$ as the sum and product of its zeros respectively then the quadratic polynomial f(x) is
  • A. $$x^2-2x-4$$
  • B. $$4x^2-2x+1$$
  • C. $$2x^2+4x-1$$
  • D. $$2x^2-4x-1$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Q10 Single Correct Medium
If one of the zeros of the cubic polynomial $$x^3 + ax^2 + bx + c$$ is $$-1$$, then the product of the other two zeros is
  • A. $$b - a - 1$$
  • B. $$a - b + 1$$
  • C. $$a - b - 1$$
  • D. $$b - a + 1$$

Asked in: Mathematics - Polynomials


1 Verified Answer | Published on 25th 08, 2020

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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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