Question

Find the quadratie polynomial whose sum and product of zeros are respectively V2 and 1/3​

Answer 1

Answer:

$\frac{k}{6}$ ( 6x² + 3x - 2 ) where k is a real number.

Step-by-step explanation:

Sum of zeroes = α + β =  1/2

Product of zeroes = αβ = 1/3

∴ the polynomial is = k ( $x^{2} + (\alpha +\beta )x - \alpha \beta )$ where k is a real number.

⇒ k ( $x^{2} + (\frac{1}{2} )x - \frac{1}{3} )$

⇒ k (  x² + $\frac{1}{2}$x - $\frac{1}{3}$ )

⇒ k ( $\frac{6x^{2} + 3x - 2}{6}$ )

∴ The polynomial is: $\frac{k}{6}$ ( 6x² + 3x - 2 ) where k is a real number.

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