Q.1 Find the sum and product of the zeroes of each of the polynomials
(i) x2 + 7x + 10
(ii) 5x2 – 7x + 2
(iii) x2 –3
(iv) 3x2 – 4x – 4
(v) x2 + 4x
Answers
Step-by-step explanation:
sumofthezeroes=35productofzeroes=2
Step-by-step explanation:
\begin{gathered}Let\:us\: assume \:\alpha\\and\:\beta \:are \: zeroes\:of\\given\: polynomial\:3x^{2}-5x+6.\\compare\:this \:with\\ax^{2}+bx+c,\:we\:get\end{gathered}Letusassumeαandβarezeroesofgivenpolynomial3x2−5x+6.comparethiswithax2+bx+c,weget
a=3,\:b=-5,\:c=6a=3,b=−5,c=6
\begin{gathered}Now,\\sum\:of\:the \: zeroes\\=\frac{-b}{a}\end{gathered}Now,sumofthezeroes=a−b \begin{gathered}\implies \alpha+\beta=\frac{-(-5)}{3}\\=\frac{5}{3}\end{gathered}⟹α+β=3−(−5)=35
\begin{gathered} Product\:of\:the\: zeroes\\=\frac{c}{a}\end{gathered}Productofthezeroes=ac
\begin{gathered}\implies \alpha\beta=\frac{6}{3}\\=2\end{gathered}⟹αβ=36=2
Therefore,
\begin{gathered}sum\:of\:the \: zeroes=\frac{5}{3}\\product \:of\: zeroes = 2\end{gathered}sumofthezeroes=35productofzeroes=2
answer is (ii)
i hope its helpfull