Question

Find the quadratic polynomial for the zeroes
1/3,-2
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Answer 1

Answer:

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Answer 2

Answer:

$\huge{\boxed{\sf{3x^{2}+5x-2}}}$

Step-by-step explanation:

$\huge{\boxed{\sf{SOLUTION-}}}$

$\alpha=\frac{1}{3}\\\beta=-2\\sum \: of \: zeroes ( \alpha + \beta ) = \frac{1}{ 3} -2\\=\frac{1-6}{3} \\\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{-5}{3}\\ product \: of \: zeroes( \alpha \beta ) = \frac{1}{3}\times-2\\\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{-2}{3}\\ > > according \: the \: question \: \\ > > forming \: quadratic \: eqn \: by \: given \: zeroes \\ {x}^{2} - ( sum \: of \: zeroes)x + (product \: of \: zeroes) = 0 \\ {x}^{2} - ( \alpha + \beta)x + ( \alpha \beta ) = 0 \\ = ) {x}^{2} - \frac{-5}{3} x +( \frac{-2}{3} ) = 0 \\ = ) {x}^{2} - \frac{-5}{3}x - \frac{2}{3}= 0 \\ = ) { 3{x}^{2} +5x-2 } = 0 \\ = ) 3 {x}^{2} + 5x - 2 = 0$

$\huge{\boxed{\sf{3x^{2}+5x-2}}}$