Question 2 :
If one of the zeroes of the cubic polynomial $x^3+ax^2+bx+c$ is -1, then the product of other two zeroes is:
Question 3 :
If the zeroes of the quadratic polynomial $x^2+\left(a+1\right)x+b$ are 2 and -3, then:
Question 4 :
If $x^2+2x+k$ is a factor of $2x^4+x^3-14x^2+5x+6$. Find all the zeroes of the two polynomials
Question 7 :
Find all the zeros of $2x^4-3x^3-3x^2+6x-2$, if you know that two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$ .
Question 8 :
Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt{2}$ and $\frac{1}{3}$, respectively.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a52273b230584979920.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 10 :
The zeroes of the quadratic polynomial, whose sum and product of the zeroes are $\sqrt{2}$ and $-\frac{3}{2}$ respectively, are:
Question 11 :
If on division of a polynomial $p\left(x\right)$ by a polynomial $g\left(x\right)$, the quotient is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be4273b230584979a3a.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 13 :
If the zeroes of $q\left(x\right)=x^3+2x^2+a$ are also the zeroes of the polynomial $p\left(x\right)=x^5-x^4-4x^3+3x^2+3x+b$ Which zeroes of $p\left(x\right)$ are not the zeroes of $q\left(x\right)$?
Question 15 :
Can $x-1$ be the remainder on division of a polynomial $p\left(x\right)$ by $2x+3$ ?
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be5273b230584979a3b.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 18 :
State true or false: The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be1273b230584979a36.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 20 :
Given that the $\sqrt{2}$ is a zero of the cubic polynomial $6x^3+\sqrt{2}x^2-10x-4\sqrt{2}$, find its other two zeroes
Question 21 :
Divide $3x^{3}+x^{2}+2x+5$ by $1+2x+x^{2}$. The quotient is $3x–5$ and the remainder is $9x+10$. Is it correct?
Question 24 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{8}{3}$, $\frac{4}{3}$
Question 26 :
What will the remainder be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?
Question 27 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-2\sqrt{3}$, -9
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be7273b230584979a3d.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 30 :
The zeroes of the polynomial $x^4-6x^3-26x^2-138x-35$ are $2\pm \sqrt {3}$, 7, -5.
Question 31 :
Divide $3x^2 – x^3 – 3x + 5$ by $x – 1 – x^2$ and find the remainder and the quotient?
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a57273b230584979925.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 33 :
What will the quotient be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?
Question 34 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-2\sqrt{3}$, -9
Question 35 :
If the zeroes of the quadratic polynomial $ax^2+bx+c$, $c\ne0$ are equal, then:
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4f273b23058497991c.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 37 :
Find a quadratic polynomial, the sum and product of whose zeroes are $-\frac{1}{4}$ and $\frac{1}{4}$ , respectively.
Question 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be8273b230584979a3e.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 39 :
Divide $3x^2 – x^3 – 3x + 5$ by $x – 1 – x^2$ and find the remainder. Is the remainder independent of $x$ ?
Question 40 :
Divide $2x^{2}+3x+1$ by $x+2$. What would be the quotient and remainder respectively?
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a50273b23058497991d.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 42 :
If the polynomial $x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2– 2x+k$, the remainder comes out to be x + a, then k and a are 5 and -5 respectively.
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a54273b230584979922.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 45 :
State true or false: The only value of $k$ for which the quadratic polynomial $kx^2+x+k$ has equal zeroes is $\frac{1}{2}$.
Question 46 :
Are the numbers given alongside of the cubic polynomials their zeroes? $2x^3+x^2-5x+2$; $\frac{1}{2}$, 1, -2 .
