Question Text
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 :
Find a quadratic polynomial, the sum and product of whose zeroes are $-\frac{1}{4}$ and $\frac{1}{4}$ , respectively.
Question 3 :
Are the numbers given alongside of the cubic polynomials their zeroes? $x^3-4x^2+5x-2$; 2, 1, 1.
Question 5 :
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 6 :
The zeroes of $3x^4+6x^3–2x^2–10x–5$ are $\sqrt{\frac{5}{3}}$, $-\sqrt{\frac{5}{3}}$, -1 and -1. Is it true or false?
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 :
Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Question 10 :
<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 $p\left(x\right)$.