Question

find a quadratic polynomial whose sum and product of zeroes are 4 and 1
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Answer 1

Answer:

α+β=4

αβ=1

required polynomial=k(x²-(α+β)x+αβ)

                              =k(x²-4x+1)

required polynomial is x²-4x+1 where k=1

Answer 2

Answer:

THE FORMULA TO FIND QUADRATIC POLYNOMIAL IS

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

THE QUADRATIC POLYNOMIAL

${x}^{2} - 4x + 1$

Step-by-step explanation:

$k( {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) \\ k( {x}^{2} - (4)x + (1) \\ when \: there \: is \: no \: denominator \: in \\ the \: given \: values \: then \: the \: k \: value \\ \: becomes \: \: \: \: \: 1 \: \\ therefore \\ 1( {x}^{2} - 4x + 1) \\ {x}^{2} - 4x + 1$

HOPE IT HELPS YOU

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