Polynomial Mastery: The Ultimate Grade 10 Challenge

Interactive Quiz: Polynomial Mastery: The Ultimate Grade 10 Challenge

Polynomial Mastery: The Ultimate Grade 10 Challenge

Test your deep understanding of polynomials, from the relationship between zeroes and coefficients to the division algorithm and beyond.

Question 1 of 10

If the zeroes of the cubic polynomial $x^{3} - 3x^{2} + x + 1$ are $a - d$, $a$, and $a + d$, what are the values of $a$ and $d$?

$a = 1$, $d = \pm \sqrt{2}$

$a = 1$, $d = \pm 2$

$a = -1$, $d = \pm \sqrt{2}$

$a = 2$, $d = \pm 1$

Question 2 of 10

The polynomial $p(x) = x^{4} - 6x^{3} + 16x^{2} - 25x + 10$ is divided by another polynomial $x^{2} - 2x + k$. If the remainder is $x + a$, find the values of $k$ and $a$.

$k = 5$, $a = -5$

$k = -5$, $a = 5$

$k = 2$, $a = -3$

$k = 5$, $a = 5$

Question 3 of 10

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^{2} - p(x + 1) - c$, find the value of $(\alpha + 1)(\beta + 1)$.

$1 - c$

$c - 1$

$p - c$

$1 + c$

Question 4 of 10

Find all the zeroes of $2x^{4} - 3x^{3} - 3x^{2} + 6x - 2$, if you know that two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$.

$\sqrt{2}, -\sqrt{2}, 1, \frac{1}{2}$

$\sqrt{2}, -\sqrt{2}, -1, \frac{1}{2}$

$\sqrt{2}, -\sqrt{2}, 1, -\frac{1}{2}$

$\sqrt{2}, -\sqrt{2}, 2, \frac{1}{2}$

Question 5 of 10

If $\alpha, \beta, \gamma$ are the zeroes of the polynomial $f(x) = ax^{3} + bx^{2} + cx + d$, then the value of $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ is:

$-\frac{c}{d}$

$\frac{c}{d}$

$-\frac{b}{d}$

$\frac{b}{d}$

Question 6 of 10

If the sum of the zeroes of the quadratic polynomial $f(t) = kt^{2} + 2t + 3k$ is equal to their product, find the value of $k$.

$k = -\frac{2}{3}$

$k = \frac{2}{3}$

$k = -\frac{3}{2}$

$k = 0$

Question 7 of 10

If $\alpha$ and $\beta$ are zeroes of the polynomial $x^{2} - x - k$ such that $\alpha - \beta = 9$, find the value of $k$.

$k = 20$

$k = -20$

$k = 10$

$k = -10$

Question 8 of 10

If the zeroes of the polynomial $f(x) = x^{3} - 12x^{2} + 39x - 28$ are in Arithmetic Progression, find the common difference $d$ if the first term $a$ is the smallest zero.

$3$

$4$

$1$

$2$

Question 9 of 10

What is the number of zeroes of a polynomial whose graph is parallel to the $x$-axis and does not coincide with it?

$0$

$1$

Infinite

Not defined

Question 10 of 10

If $\alpha, \beta$ are zeroes of $x^{2} - 6x + a$, find the value of $a$ if $3\alpha + 2\beta = 20$.

$a = -16$

$a = 16$

$a = -8$

$a = 8$

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Keywords: Grade 10 Maths, Polynomials Quiz, Quadratic Equations, Cubic Polynomials, Zeroes and Coefficients, CBSE Maths Class 10 Chapter 2, Math Problems