Question

plz give the answer now........

Answer 1

Heya !!

Let Alpha = 2/3 and Beta = -1/3

Sum of zeroes = Alpha +/Beta = 2/3 + (-1/3) = 2/3 - 1/3 = ( 2 - 1)/3 = 1/3

And,

Product of zeroes = Alpha × Beta = 2/3 × -1/3 = -2/9

Therefore,

Required quadratic polynomial = X² - ( Sum of zeroes )X + Product of zeroes.

=> X² - ( 1/3)X + ( -2/9)

=> X² - X/3 - 2/9

=> 9X² - 3X - 2.

Answer 2

HEYA!!
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Given that the zeroes are 2/3 and -1/3


We need to find the polynomial .

We have
,

Sum of Zeroes = 2/3 - 1/3

= 1/3

Product of Zeroes = 2/3 × -1/3

= -2/9

Now using the formula ,

P(X) = X^2 - SX + P.

{ Here S and P denote sum and product of polynomial }

Polynomial is

X^2 - 1/3 X -2/9

$x {}^{2} - \frac{1}{3} x - \frac{2}{9 } \\ \\ \frac{9x {}^{2} - 3x - 2 }{9} = 0 \\ \\ 9x {}^{2} - 3x - 2 = 0$
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