Question

check whether 2 and 1 are the zeroes of the polynomial p(x)=x²-2x
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Answer 1

⠀⠀⠀$\huge\underline{ \mathrm{ \red{QueS{\pink{tiOn}}}}}$

check whether 2 and 1 are the zeroes of the polynomial p(x)=x²-2x

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$\Large \bf\: \underline{ \color{blue}{answer}}$

$\bf\:p(1)=-1$

1 is not a factor of given polynomial.

$\bf\:</strong><strong>p</strong><strong>(</strong><strong>2</strong><strong>)</strong><strong>=</strong><strong>0</strong><strong>$

2 is a factor of given polynomial

⠀⠀⠀$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanA{\green{TiOn }}}}}}}}$

$\large\underline{ \underline{ \red{ \bold {Given}}}}$

$\bf\:p(x)= {x}^{2}-2x$

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

we need to check that 2and 1 are the zeroes of p(x) or not.

⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \orange{ \bold{sOluTiOn}}}}$

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$\bf\:p(x)= {x}^{2}-2x \\ \\ \bf : \implies \:p(1) = 1 {}^{2} - 2 \times 1 \\ \\\bf : \implies \:p(1) = 1 - 2 \\ \\\bf : \implies \: - 1 \\ \\\bf \:so \: we \: get \: p(1) = - 1 \: not \: zero \: \\ \bf \: so \: 1 \: is \:not \: a \: factor \: of \: p(x).$

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$\bf\:p(x)= {x}^{2}-2x \\ \\ \bf : \implies \:p(2) = 2 {}^{2} - 2 \times 2 \\ \\\bf : \implies \:p(2) = 4 - 4 \\ \\ \bf : \implies \:p(2) = 0 \\ \\ \bf \: since \: p(2) = 0 \: so \: 2 \: is \:a \: factor \:\\ \bf\:of \: given \: polynomial$

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