Question 1 :
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 2 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{8}{3}$, $\frac{4}{3}$
Question 3 : <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 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a53273b230584979921.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 5 :
If the remainder on division of $x^3+2x^2+kx+3$ by $x-3$ is 21, find the quotient.
Question 6 :
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 7 :
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 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a51273b23058497991f.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 11 :
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 12 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$
Question 13 :
Can $x-1$ be the remainder on division of a polynomial $p\left(x\right)$ by $2x+3$ ?
Question 14 :
The zeroes of the polynomial $x^4-6x^3-26x^2-138x-35$ are $2\pm \sqrt {3}$, 7, -5.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a58273b230584979926.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 16 :
State true or false: If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Question 17 :
On dividing $x^3-3x^2+x+2$ by a polynomial $g\left(x\right)$, the quotient and remainder were $x–2$ and $–2x+4$, respectively. Then $g\left(x\right)$ is $x^2-x+1$.
Question 18 :
If on division of a non-zero polynomial $p\left(x\right)$ by a $g\left(x\right)$, the remainder is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?
Question 19 :
Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{1}{4}$ and -1, respectively.
Question 20 :
If the zeroes of the quadratic polynomial $ax^2+bx+c$, $c\ne0$ are equal, then:
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be3273b230584979a39.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 24 :
If one zero of the quadratic polynomial $x^2+3x+k$ is 2, then the value of $k$ is:
Question 25 :
Divide $3x^2 – x^3 – 3x + 5$ by $x – 1 – x^2$ and find the remainder. Is the remainder independent of $x$ ?
Question 26 :
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 27 :
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 28 :
Find a quadratic polynomial, the sum and product of whose zeroes are 0 and $\sqrt {5}$, respectively.
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be0273b230584979a35.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 : <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 $p\left(x\right)$
