Find a quadratic polynomial whose zeros are 5-3√2 and 5+3√2
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Answer:
x ^2 −10x+7
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If 5±3
2
are roots of polynomial then
x−(5+3
2
) and x−(5−3
2
) are factors of the polynomial
∴[x−(5+3
2
)][x−(5−3
2 )=x 2 −x(5−3 2 +5+3 2 )+(5+3 2 )(5−3 2 )
=x 2 −10x+(25−9(2))
=x 2−10x+7
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