Question

Verify the relation between the zeroes and the coefficients of3x^2-5x-8 ​

Answer 1

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Verify the relation between the zeroes and the coefficients of 3x² - 5x - 8 = 0

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★ Given polynomial,

$\bf\: ⟹ 3x^{2} - 5x - 8 = 0$

$\bf\: ⟹ 3x^{2} - 3x + 8x - 8 = 0$

$\bf\:⟹ 3x(x - 1) + 8(x - 1) = 0$

$\bf\:⟹(3x + 8)(x - 1) = 0$

$\bf\:⟹3x + 8 = 0 ; x - 1 = 0$

$\bf\:⟹3x = 0 - 8 ; x = 0 + 1$

$\bf\:⟹3x = - 8 ; x = 1$

$\bf\:⟹x = \frac{- 8}{3} ; x = 1$

Hence, the zeroes of the polynomial are -8/3 & 1

★ Let,

• α = -8/3
• ß = 1

$\underline{\boxed{\tt{∴ Sum\:of\:the\:zeroes\: = \alpha+\beta}}}$

$\bf\:⟹ \frac{-8}{3} + 1$

$\bf\:⟹ \frac{-8 + 3}{3}$

$\bf\:⟹ \frac{-5}{3}$

$\underline{\boxed{\tt{∴ Sum\:of\:the\:zeroes\: = \frac{co - efficient\:of\:x}{co - efficient\:of\:x^{2}}}}}</p><p>$

$\bf\:⟹ \frac{-5}{3}$

$\underline{\boxed{\tt{∴ Product\:of\:the\:zeroes\: = \alpha\beta}}}$

$\bf\:⟹ \frac{-8}{3} \times 1$

$\bf\:⟹ \frac{-8}{3}$

$\underline{\boxed{\tt{∴ Product\:of\:the\:zeroes\: = \frac{constant\:term}{co - efficient\:of\:x^{2}}}}}$

$\bf\:⟹ \frac{-8}{3}</p><p>$

# HENCE, IT IS VERIFIED...

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