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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

1 Verified Answer | Published on 25th 08, 2020

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

1 Verified Answer | Published on 25th 08, 2020

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. $\dfrac {4}{5}$

1 Verified Answer | Published on 25th 08, 2020

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. $\alpha+\beta=\alpha \beta$

1 Verified Answer | Published on 25th 08, 2020

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. $\dfrac {-d}{a}$

1 Verified Answer | Published on 25th 08, 2020

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. $\dfrac {13}{3}$

1 Verified Answer | Published on 25th 08, 2020

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

1 Verified Answer | Published on 25th 08, 2020

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. $\dfrac {5}{3}$

1 Verified Answer | Published on 25th 08, 2020

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. $2x^2-4x-1$

1 Verified Answer | Published on 25th 08, 2020

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. $b - a + 1$