Question

If ‘1’ is one of the zeroes of the polynomial 7x - x² -6 , find the other zeroes

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• '1' is a zero of the polynomial 7x - x² -6

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$\red{\underline \bold{To \: Find:}}$

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• The other zero of the polynomial.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{General form</p><p>}}}$

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$\red\longrightarrow$ ax² + bx + c

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Above polynomial can be rewritten in general form as,

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$\purple\longrightarrow$ - x² + 7x -6

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Here we got a quadratic polynomial.[Having degree = 2]

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$\underline{\bold{\texttt{Zeroes of quadratic polynomial}}}$

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$\bf \alpha \: \: \&\: \: \beta$

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Also,

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$\red{\bold{Sum \: of \: zeroes \: = \: \dfrac { -b } { a } }}$

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$\boxed {\rm \alpha \: \: + \: \: \beta \: = \frac { -b } { a } }$

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$\rm Let \: 1 \: be \: \alpha$

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$\sf \longmapsto 1 +\: \beta \: = \dfrac { -7 } { -1 }$

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$\sf \longmapsto \beta \: = 7 - 1$

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$\bf \dashrightarrow \beta \: = 6$

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Hence the zeroes of given polynomial are 1 & 6

$\rule{200}6$

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$\underline{\bold{\texttt{Additional information }}}$

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Product of zeroes of quadratic polynomial is $\bf \dfrac { c } { a }$

$\rule{200}5$