Question Text
Question 1 :
State true or false: If α and β are the zeroes of a quadratic polynomial $ax^{2}+bx+c$, then $α+β=-\frac{b}{a}$, $αβ=\frac{c}{a}$.
Question 2 :
<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 3 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a54273b230584979922.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 :
Find a quadratic polynomial, the sum and product of whose zeroes are 0 and $\sqrt {5}$, respectively.
Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a50273b23058497991d.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 8 :
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 9 :
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 10 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^2+3x+1$, $3x^4+5x^3–7x^2+2x+2$