Polynomials

CBSE Class 10 · Mathematics · 35 past questions

These are the board's own papers. 91 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026

The sum and product of zeroes of a quadratic polynomial p(x) are $\frac{-1}{3}$ and 2 respectively. The…
Q2 2026

If the zeroes of a polynomial p(x) are –3 and 8, then p(x) equals
Q3 2026

$\alpha$ and $\beta$ are the zeroes of the polynomial $5x^2 - 16x - 10$. Find the value of…
Q4 2026 (Basic)

If $\alpha$, $\beta$ are the zeroes of polynomial $p(x) = 6x^2 - 5x - 3$, then find the value of…
Q5 Sample paper 2026-27

If $f(x) = px^2 + qx + r$, $p \neq 0$ and $p + r = q$, then one of the zeroes of $f(x)$ is…
Q6 Sample paper 2026-27

Assertion-
Reason Based Questions…
Q7 Sample paper 2026-27

If α and β are the zeroes of the quadratic polynomial $2x^2 - 8x + 5$, then find the value of…
Q8 2025

If $-4$ is a zero of the polynomial $p(x) = x^2 - x - (2 + 2k)$, then the value of k is…
Q9 2025

If p and q are zeroes of the polynomial $p(y) = 21y^2 - y - 2$, then find the value of…
Q10 2025

If $\alpha$ and $\beta$ are the zeroes of the polynomial $p(x) = x^2 - ax - b$, then the value of…
Q11 2025

Zeroes of the polynomial p(x) = x² - 3√2 x + 4 are…
Q12 2025

Find the value(s) of 'k' so that the quadratic equation $4x^2 + kx + 1 = 0$ has real and equal roots.
Q13 2025

If $\alpha$ and $\beta$ are the zeroes of polynomial $3x^2 + 6x + k$ such that…
Q14 2025

Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is… (with a figure)
Q15 2025

Find the zeroes of the polynomial $p(x) = x^2 + \frac{4}{3}x - \frac{4}{3}$.
Q16 2025 (Basic)

Find a quadratic polynomial whose sum and product of zeroes are 0 and $-9$, respectively. Also, find the…
Q17 2024

Find the zeroes of the quadratic polynomial $x^2 - 15$ and verify the relationship between the zeroes and the…
Q18 2024

If $\alpha$ and $\beta$ are zeroes of the polynomial $5x^2 + 3x - 7$, the value of…
Q19 2024

If the sum of zeroes of the polynomial $p(x) = 2x^2 - k\sqrt{2}x + 1$ is $\sqrt{2}$, then value of $k$ is…
Q20 2024

The zeroes of a polynomial $x^2 + px + q$ are twice the zeroes of the polynomial $4x^2 - 5x - 6$. The value…
Q21 2024

Directions : In Q. No. 19 and 20 a statement of Assertion (A) is followed by a statement of Reason (R).…
Q22 2024 (Basic)

For what value of $k$, the product of zeroes of the polynomial $kx^2 - 4x - 7$ is 2 ?
Q23 2024 (Basic)

If one of the zeroes of the quadratic polynomial $(\alpha-1)x^2+\alpha x+1$ is $-3$, then the value of…
Q24 2024 (Basic)

Directions : In Q. No. 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).…
Q25 2023

If one zero of the polynomial $6x^2 + 37x - (k - 2)$ is reciprocal of the other, then what is the value of k ?
Q26 2023

The zeroes of the polynomial p(x) = x$^2$ + 4x + 3 are given by…
Q27 2023

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial p(x) = x$^2$ $-$ ax $-$ b, then the value…
Q28 2023

If $\alpha, \beta$ are zeroes of the polynomial $x^2 - 1$, then value of $(\alpha + \beta)$ is…
Q29 2023

If $\alpha, \beta$ are the zeroes of the polynomial p(x) = $4x^2 - 3x - 7$, then…
Q30 2023

If one zero of the polynomial p(x) = $6x^2 + 37x - (k - 2)$ is reciprocal of the other, then find the value…
Q31 2023

The graph of y = p($x$) is given, for a polynomial p($x$). The number of zeroes of p($x$) from the graph is (with a figure)
Q32 2023

If $\alpha, \beta$ are the zeroes of a polynomial $p(x) = x^2 + x - 1$, then…
Q33 2023

Which of the following is a quadratic polynomial having zeroes $\dfrac{-2}{3}$ and $\dfrac{2}{3}$ ?
Q34 2023 (Basic)

The sum and the product of zeroes of the polynomial $p(x) = x^2 + 5x + 6$ are respectively
Q35 2023 (Basic)

If $\alpha$, $\beta$ are zeroes of the quadratic polynomial $x^2 + 3x + 2$, find a quadratic polynomial whose…