Question 1 :
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 2 : <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 3 :
Given that $x-\sqrt{5}$ is a factor of the cubic polynomial $x^3-3\sqrt{5}x^2+13x-3\sqrt{5}$, find all the zeroes of the polynomial
Question 4 : <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 5 :
Can $x-1$ be the remainder on division of a polynomial $p\left(x\right)$ by $2x+3$ ?
Question 6 :
Find a quadratic polynomial whose sum and product
respectively of the zeroes are as given: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdf273b230584979a34.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 8 :
Divide $2x^{2}+3x+1$ by $x+2$. What would be the quotient and remainder respectively?
Question 10 :
If one of the zeroes of the quadratic polynomial of the form $x^2+ax+b$ is the negative of the other, then it:
Question 12 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^4–3x^2+4x+5$, $g\left(x\right)$ = $x^2+1-x$
Question 13 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{8}{3}$, $\frac{4}{3}$
Question 14 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-2\sqrt{3}$, -9
Question 15 :
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 16 :
Given that the zeroes of the cubic polynomial $x^3-6x^2+3x+10$ are of the form a, a+b, a+2b for some real numbers a and b, find the value of b.
Question 17 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-2\sqrt{3}$, -9
Question 18 :
The quadratic polynomial whose sum and product of zeros being $\sqrt{2}$ and $-\frac{3}{2}$ respectively, is:
Question 19 :
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 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a56273b230584979924.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 21 :
If one of the zeroes of the quadratic polynomial $\left(k-1\right)x^2+kx+1$ is -3, then the value of k is:
Question 23 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $t^2–3$, $2t^4+3t^3–2t^2–9t–12$
Question 24 :
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 25 :
Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Question 26 : <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 27 :
Is the statement true or false? If the zeroes of a quadratic polynomial $ax^2+bx+c$ are both negative, then, a, b and c all have the same sign.
Question 28 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^3-3x+1$, $x^5–4x^3+x^2+3x+1$
Question 29 :
If the zeroes of the quadratic polynomial $ax^2+bx+c$, $c\ne0$ are equal, then:
