Which of the following is a true statement?
- A$x^2 + 5x - 3$ is a linear polynomial.
- B$x^2+ 4x - 1$ is a binomial.
- C$x + 1$ is a monomial.
- ✓$5x^3$ is a monomial.
Answer: D.
View full solution →Question types
Polynomials question types
140 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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Sample Questions
Polynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\alpha$ and $\beta$ are the zero of $2x^2 + 5x − 8,$ then the value of $(\alpha\beta)$ is:
- A$\frac{-5}{2}$
- B$\frac{5}{2}$
- ✓$\frac{-9}{2}$
- D$\frac{9}{2}$
Answer: C.
View full solution →The zeros of the polynomial $\text{x}^2+\frac{1}{6}\text{x}-2$ are:
- A$-3,\ 4$
- ✓$\frac{-3}{2},\ \frac{4}{3}$
- C$\frac{-4}{3},\ \frac{3}{2}$
- DNone of these.
Answer: B.
View full solution →If $\alpha,\ \beta$ are the zeros of $kx^2 - 2x + 3k$ such that $\alpha+\beta=\alpha\beta,$ then $k = ?$
- A$\frac{1}{3}$
- B$\frac{-1}{3}$
- ✓$\frac{2}{3}$
- D$\frac{-2}{3}$
Answer: C.
View full solution →The zeros of the polynomial $x^2 - 2x - 3$ are:
- A$-3, 1$
- B$-3, -1$
- ✓$3, -1$
- D$3, 1$
Answer: C.
View full solution →The graph of the polynomial $f(x)=a x^2+b x+c$ is as shown in Fig. Write the value of $b^2-4 a c$ and the number of real zeros of $f(x)$, write the sign of $c$.
View full solution →Write the standard form of a quadratic polynomial with real coefficients.
The graph of the polynomial $f(x) = ax^2 + bx + c$ is as shown in Fig. Write the value of $b^2 - 4ac$ and the number of real zeros of $f(x). $
View full solution →If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?
Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.
View full solution →Give an example of polynomials $f(x), g(x), q(x)$ and $r(x)$ satisfying $f(x) = g(x), q(x) + r(x)$, where degree $r(x) = 0.$
View full solution →If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = ax^2 + bx + c$, then evaluate:$\alpha^4+\beta^4$
View full solution →For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.
$\frac{21}{8},\frac{5}{16}$
View full solution →$\frac{21}{8},\frac{5}{16}$
If $a - b$, $a$ and $b$ are zeros of the polynomial $f(x) = 2x^3- 6x^2 + 5x - 7$, write the value of a.
View full solution →What must be added to the polynomial $f(x) = x^4 + 2x^3 - 2x^2 + x - 1$ so that the resulting polynomial is exactly divisible by $x^2 + 2x - 3$?
View full solution →For what value of $k, -4$ is a zero of the polynomial $x^2 - x - (2k + 2)$?
View full solution →If the zeros of the polynomial $f(x) = ax^3 + 3bx^2 + 3cx + d$ are in A.P., prove that $2b^3 - 3abc + a^2d = 0.$
View full solution →If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f(x) = x^2 - px + q$, prove that $\frac{\alpha^2}{\beta^2}+\frac{\beta^2}{\alpha^2}=\frac{\text{p}^2}{\text{q}}-\frac{4\text{p}^2}{\text{q}}+2.$
View full solution →Find all zeros of the polynomial $f(x) = 2x^4 - 2x^3 - 7x^2 + 3x + 6$,
if its two zeros are $-\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{3}{2}}$
View full solution →if its two zeros are $-\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{3}{2}}$
If the zeros of the polynomial $f(x) = 2x^3 - 15x^2 + 37x - 30$ are in A.P., find them.
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