Sum of zeroes = α + β =√2
Product of zeroes = α β = 1/3
∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-
x2–[α+β]x +αβ = 0
x2 –[√2]x + [1/3] = 0
3x2-3√2x+1 = 0
Thus, 3x2-3√2x+1 is the quadratic polynomial.
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Solution
Let the zeroes be α and β
According to the question:
α+β=−3and αβ=2
The quadratic polynomial whose sum and product of the zeroes are given is given by :
x²−[α+β]x+αβ
⇒ Then the quadratic polynomial will be :
⇒ x²−[−3]x+2
⇒x²+3x+2
Hence, the quadratic polynomial is
x2+3x+2
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