Question

If a and b are two zeroes are quadratic polynomial 2x² - 3x 7. The value of a³ + b³ is?

Answer 1

$Given \: 'a' \: and \: 'b' \: are \:two\: zeroes$

$of\: Quadratic \: polynomial \: 2x^{2}-3x+7$

$i) Sum \: of \: zeroes = \frac{- Coefficient \: of\:x^{2}}{ Coefficient \: of \: x }$

$= \frac{ -(-3)}{2}$

$= \frac{3}{2} \: --(1)$

$ii) Product \: of \: zeroes = \frac{Constant \:term}{ Coefficient \: of \: x }$

$= \frac{ 7}{2} \: ---(2)$

$\red{ Value \:of \: a^{3} + b^{3} }$

$= ( a + b )^{3} - 3ab (a+b)$

$= \Big( \frac{3}{2}\Big)^{3} - 3 \times\frac{7}{2} \times \frac{3}{2}$

$= \frac{27}{8} - \frac{63}{4}$

$= \frac{ 27 - 126}{8}$

$= \frac{-99}{8}$

Therefore.,

$\red{ Value \:of \: a^{3} + b^{3} } \green { =\frac{-99}{8}}$

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