Question

If α and β are the zeroes of quadratic polynomial 3x2 + 2x – 7, then the value of (α – 3)(β – 3) is 1at answer will be brainest

Answer 1

Answer:

answer for the given problem is given

Answer 2

$Given \: \alpha \:and \:\beta \: are \: the\: zeroes$

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

$Compare \: above \: polynomial \: with$

$ax^{2} + bx+c , we \:get$

$a = 3, \: b = 2 \: and \: c = - 7$

$i) \alpha + \beta = \frac{-b}{a}$

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

$ii) \alpha \beta = \frac{c}{a}$

$= \frac{ -7}{3} \: --(2)$

$Now, \red{ Value \: of \: (\alpha - 3)(\beta-3) }$

$= \alpha(\beta-3) -3(\beta-3)$

$= \alpha \beta - 3(\alpha+\beta) +9$

$= \frac{ -7}{3}-3\times \Big(\frac{ -2}{3}\Big)+9$

$= \frac{-7 + 6 + 27 }{3}$

$= \frac{-7+33}{3}$

$= \frac{26}{3}$

Therefore.,

$\red{ Value \: of \: (\alpha - 3)(\beta-3) }$

$\green{= \frac{26}{3}}$

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