Question

find the zeroes of the quadratic polynomial P( x )=x²+x-12and verify the relationship between the zeroes and the coefficients
Plz answer and be brainliest ​

Answer 1

zeros of polynomials are -4 and 3

and verification are done in above page☝️

Answer 2

AnswEr :

⠀

$\star\;\bold{\underline{\sf{\purple{Given\: Polynomial\: : \: x^2 + x - 12\; }}}}$⠀⠀

⠀

$\dashrightarrow\sf x^2 + 4x - 3x - 12 = 0 \\\\\\\dashrightarrow\sf x\Big\{x + 4\Big\} -3\Big\{x + 4\Big\} =0\\\\\\\dashrightarrow\sf \Big\{x + 4\Big\} \Big\{x - 3\Big\}=0\\\\\\\dashrightarrow\underline{\boxed{\frak{\purple{x = -4\:\&\;3}}}}\;\bigstar$

⠀

$\therefore{\underline{\textsf{Hence,\;the\; zeroes\;of\;the\;given\; polynomial\;are\; \textbf{-4 and 3}.}}}$

$\rule{300px}{.4ex}$

⠀

$\qquad\quad{\underline {\dag \: \textbf{Relation b/w Coefficients \& Zeroes \: :}}}$⠀⠀

⠀

${\qquad\maltese\:\:\textsf{Sum of Zeroes :}} \\\\\dashrightarrow\sf\:\:\alpha +\beta= \dfrac{ - \:b \: \: \: }{ \: \: \: a \: \: \:}\\\\\\\dashrightarrow\sf \Big\{-4 + 3\Big\} = \bigg\{\dfrac{-1}{\;1}\bigg\} \\\\\\\dashrightarrow\underline{\boxed{\frak{-1 = -1}}}$

⠀⠀⠀

${\qquad\maltese\:\:\textsf{Product of Zeroes :}}\\\\\dashrightarrow\sf\:\:\alpha\beta=\dfrac{c}{a}\\\\\\\dashrightarrow\sf \Big\{-4 \times 3\Big\} = \bigg\{\dfrac{-12}{\; 1}\bigg\}\\\\\\\dashrightarrow\underline{\boxed{\frak{-12 = -12}}}$

⠀

$\qquad\qquad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$