Question Text
Question 1 :
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 2 :
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 3 : <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 4 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-2\sqrt{3}$, -9
Question 6 :
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 7 :
Find a quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively.
Question 8 :
Find the zeroes of the quadratic polynomial $3x^{2} + 5x - 2$.
Question 9 :
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 10 :
If the remainder on division of $x^3+2x^2+kx+3$ by $x-3$ is 21, find the quotient.
