Question

find the zeros of the quadratic polynomial and verify the relation between the zeros and the coefficients 4u square + 8u

Answer 1

нere'ѕ yoυr ѕolυтιon

Answer 2

$\huge\sf\blue{Given}$

☞ 4u² + 8u

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$\huge\sf\gray{To \:Find}$

➢ It's zeros and the relationship between the zeros and coefficients

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$\huge\sf\purple{Steps}$

$\underline{\bigstar\:\textsf{Zeroes \: of \: Polynomial:}}\\ \\ \\ \normalsize\dashrightarrow\sf\ 4u^2 + 8u = 0 \\ \qquad\footnotesize\star\sf\ Using \: Middle \: term \: factorization \\\\\\\normalsize\dashrightarrow\sf\ 4u(u + 2) = 0\\\\\\\normalsize \dashrightarrow\sf\ 4u = 0 \: \: or \: \: (u + 2) = 0\\\\\\\normalsize \dashrightarrow\sf\ u = \frac{0}{4} \: \: or \: \: 0 - 2\\\\\\\normalsize \dashrightarrow\sf\ u = 0 \: \: or \: \: -2\\\\\\\normalsize \dashrightarrow{\underline{\boxed{\sf \red{u = 0, -2}}}}\\\\\therefore\underline{\textsf{The \: Zeroes \: of \: Polynomial \: are \: }{\textbf{0, -2 }}}$

$\underline{\bigstar\:\sf{Relationship \: b/w \: zeroes \: \& \: Polynomial:}}\\\\\qquad\begin{aligned}\bf{\dag}\:\:\bf Sum \: of \: Zeroes\:\:\quad\end{aligned}\\\normalsize\dashrightarrow\sf\ \alpha + \beta = \frac{-b}{a}\\\\\\\normalsize\dashrightarrow\sf\ 0 + (-2) = \frac{{-8}}{{4}}\\\\\\\normalsize\dashrightarrow\sf\ -2 = -2\\\\\\\normalsize\dashrightarrow{\underline{\boxed{\sf \green{-2 = - 2}}}}\\\\\qquad\begin{aligned}\bf{\dag}\:\:\bf Product \: of \: Zeroes\:\:\quad\end{aligned}\\\normalsize\dashrightarrow\sf\ \alpha + \beta = \frac{c}{a}\\\\\\\normalsize\dashrightarrow\sf\ 0 \times\ (-2) = \frac{\cancel{0}}{\cancel{4}}\\\\\\\normalsize\dashrightarrow\sf\ 0 = 0\\\\\\\normalsize\dashrightarrow{\underline{\boxed{\sf \green{0 = 0}}}}\\\\\qquad\begin{aligned}\:\:\bf{Hence, Verified!!}\:\:\quad\end{aligned}$

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