Question Text
Question 1 :
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 2 :
<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 3 :
The quadratic polynomial whose sum and product of zeros being $\sqrt{2}$ and $-\frac{3}{2}$ respectively, is:
Question 8 :
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 9 :
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 10 :
State true or false: If α and β are the zeroes of a quadratic polynomial $ax^{2}+bx+c$, then $α+β=-\frac{b}{a}$, $αβ=\frac{c}{a}$.