Question

find the zeros of the polynomial 5x^2+12x+7 and verify the relationship between the zeros and the coefficient​

Answer 1

Answer:

answer is in the attached image

Answer 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆Given Polynomial : 5x² + 12x + 7 :

⠀⠀⠀

$:\implies\sf 5x^2 + 12x + 7 = 0 \\\\\\:\implies\sf 5x^2 + 5x + 7x + 7 = 0 \\\\\\:\implies\sf 5x(x + 1) + 7(x + 1) = 0 \\\\\\:\implies\sf ( x + 1) (5x + 7) = 0 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = -1 \; \&\; \dfrac{-7}{\;5}}}}}}\;\bigstar$

$\sf{\therefore\; Zeroes\; of \; the \: Given \; polynomial \; are \; -1 \:\&\; \dfrac{-5 \: }{\; \: 7 \: }.}$

$\rule{250px}{.3ex}$

$\bf{\dag} \: \: \underline{\textsf{Relation b/w Coefficients \& Zeroes \: :}}$

⠀⠀⠀⠀⠀

${\qquad\maltese\:\:\textsf{Sum of Zeroes :}} \\\\\dashrightarrow\sf\:\:\alpha +\beta= \dfrac{ - \:b \: \: \: }{ \: \: \: a \: \: \:}\\\\\\\dashrightarrow\sf \bigg(-1\bigg) + \bigg(\dfrac{-7}{ \: \: 5}\bigg) = \dfrac{-12}{5} \\\\\\\dashrightarrow{\underline{\boxed{\frak{\dfrac{-12}{5} = \dfrac{-12}{5}}}}}$

⠀⠀⠀

${\qquad\maltese\:\:\textsf{Product of Zeroes :}}\\\\\dashrightarrow\sf\:\:\alpha\beta=\dfrac{c}{a}\\\\\\\dashrightarrow\sf \bigg(-1\bigg) \times \bigg(\dfrac{-7 \: \: }{ \: \: 5 \: \: }\bigg) = \dfrac{7 \: \: }{ \: \: 5 \: \: } \\\\\\\dashrightarrow{\underline{\boxed{\frak{\dfrac{7}{\;5} = \dfrac{7}{\;5}}}}}$

⠀⠀⠀

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

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀