Question

find the quadratic plynomial, the sum and the product of whose zeros 3 & 2 respectively
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Answer 1

Answer:

the general formula is

x²-(sum of roots)x + (products of roots)

x²-3x+2 = 0

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Answer 2

$\mathsf\red{The \: quadratic \: expression \: when \: \alpha \: and \: \beta are \: the \: roots}$

$\mathsf{ {x}^{2} - ( \alpha + \beta)x + \alpha. \beta }$

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$\mathsf\red{Given}$

$\mathsf{\alpha + \beta \: = \: 3}$

$\mathsf{\alpha . \beta \: = \: 2}$

$\mathsf\red{Substitue \: \alpha , \beta \: in \: above \: equation}$

$\mathsf{ {x}^{2} - (3).x + (2)} \\ = \: \: \: \mathsf{ {x}^{2} - 3x + 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\mathsf\red{\therefore \: {x}^{2}-3x+2 \: is \: the \: required \: equation}$

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