Question

If the zeroes of polynomial are 3x2 - 5x +2 are α+β and α-β find α and β

Answer 1

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Answer 2

Solution :

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Given :

The zeroes of polynomial are 3x² - 5x + 2 are α + β and α - β,.

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To find :

The value of α & β,.

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We know that sum of the zeroes of the polynomial of the form,.

⇒ ax² + bx + c = 0,.

(here a = 3, b = -5 , c = 2)

⇒ Sum of the zeroes = $\frac{-b}{a}$

⇒ $( \alpha + \beta ) + ( \alpha - \beta ) = \frac{-(-5)}{3}$

⇒ $2 \alpha = \frac{5}{3}$

⇒ $\alpha = \frac{5}{6}$

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⇒ Product of the zeroes = $\frac{c}{a}$

⇒ $( \alpha + \beta )( \alpha - \beta ) = \frac{2}{3}$

⇒ $\alpha ^2 - \beta ^2 = \frac{2}{3}$

⇒ $( \frac{5}{6})^2 - \beta ^2 = \frac{2}{3}$

⇒ $\frac{25}{36} - \beta^2 = \frac{2}{3}$

⇒ $- \beta ^2 = \frac{2}{3} - \frac{1}{36}$

⇒ $- \beta^2 = \frac{24}{36} - \frac{25}{36}$

⇒ $- \beta^2 = \frac{-1}{36}$

⇒ $\beta^2 = \frac{1}{36}$

⇒ $\beta = \frac{1}{6}$ (or) $\beta = - \frac{1}{6}$

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