Question

Write a quadratic polynomial with α+β=3 and α×β=2.

Answer 1

Answer:

x²+(αβ)-(α+β)x

putting the value

We get

x²+2-3x

x²-3x+2

Step-by-step explanation:

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Answer 2

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

$\green{\tt{\therefore{Quadratic\:polynomial=x^{2}-3x+2}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{Given:}} \\ \tt{: \implies \alpha + \beta = 3} \\ \\ \tt{: \implies \alpha \times \beta = 2} \\ \\ \red {\underline \bold{To \: Find:}} \\ \tt{: \implies Quadratic \: polynomial =?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) = 0} \\ \\ \tt{\circ \: Sum \: of \: zeroes( \alpha + \beta ) = 3} \\ \\ \tt{\circ \: Product\: of \: zeroes( \alpha \times \beta ) = 2}\\ \\ \text{Putting \: given \: values} \\ \tt{: \implies {x}^{2} - 3x + 2 = 0} \\ \\\tt{\huge{\red{Verification}}} \\ \\ \tt{: \implies {x}^{2} - 3x + 2 = 0} \\ \\ \bold{As \: we \: know \: that} \\ \\ \tt{\circ \:a = 1} \\ \\ \tt{\circ \:b= - 3}\\ \\ \tt{\circ \:c = 2} \\ \\ \bold{ For\:sum \: of \: zeroes}\\ \tt{: \implies Sum \: of \: zeroes = \frac{ - b}{a} } \\ \\ \tt{: \implies Sum \: of \: zeroes= \frac{ -( - 3)}{1} } \\ \\ \tt{: \implies Sum \: of \: zeroes = 3} \\ \\ \bold{For \: product \: of \:zeroes} \\ \tt{: \implies Product \: of \: zeroes = \frac{ c}{a} } \\ \\ \tt{: \implies Product \: of \: zeroes = \frac{2}{1} } \\ \\ \tt{: \implies Product \: of \: zeroes = 2 } \\ \\ \green{\huge{ \tt{Verified}}}$