find a quadratic polynomial whose zeros are (3+√2) and (3-√2)
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let the sum of zeroes be (3-√2 )
product of zeroes be (3+√2)
the polynomial be
x^2-x(sum of zeroes )+product of zeroes
x^2-x(3+√2)+(3-√2)
product of zeroes be (3+√2)
the polynomial be
x^2-x(sum of zeroes )+product of zeroes
x^2-x(3+√2)+(3-√2)
Answered by
2
alpha = 3+✓2 , Beta = 3-✓2.
Alpha + Beta = 3+✓2+3-✓2 = 6
Alpha × Beta = (3+✓2)(3-✓2) = (3)²+(✓2)²-2× 3 × ✓2.
= 9 + 2-6✓2 = 11-6✓2...
REQUIRED POLYNOMIAL = X²-(Alpha+ Beta) X+ Alpha × Beta
Alpha + Beta = 3+✓2+3-✓2 = 6
Alpha × Beta = (3+✓2)(3-✓2) = (3)²+(✓2)²-2× 3 × ✓2.
= 9 + 2-6✓2 = 11-6✓2...
REQUIRED POLYNOMIAL = X²-(Alpha+ Beta) X+ Alpha × Beta
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