find aquadratice polynomi
si al in ac, whose sum of zeroes
and product
of
zeroes are
-5/3or unde respectively.
3
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Answer:
Now,
Sum of roots = α²/β + β²/ α = α³+β³/αβ
= (α + β)³-3αβ(α+β)/αβ
= (4/3)³-3(1/3)(4/3) / 1/3
= 64/27 - 4/3 / 1/3
= 64/27-36/27 / 1/3
= 28/27 * 3/1
= 28/9
Product of roots = (α²/β * β²/ α) = (αβ ) = 1/3 .
The quadratic equation with required roots = x²-28/9x + 1/3 = 9(x² - 28/8x+1/3) = 9x² - 28x + 3
Hope helped
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