Question

If alpha and beta are the zeroes of the quadratic polynomial (x) = 3x2 + x − 6, then find a quadratic polynomial whose zeroes are ( alpha + beta ) and alpha beta

Answer 1

Answer:

hope this helps you.....

Answer 2

$Compare \: Quadratic \: polynomial$

$p(x) = 3x^{2} +x - 6 \: with\: ax^{2} + bx +c ,$

$we \: get$

$a = 3 , b = 1 \: and \: c = -6$

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

$Zeroes \: of \: p(x)$

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

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

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

$= \frac{-6}{3}$

$= -2 \: --(2)$

$\blue{ If \: \alpha + \beta \: and \: \alpha \beta \: are }$

$\blue{zeroes \: of \: a \: Quadratic \: polynomial }$

$iii ) Sum \: of \: the \: zeroes$

$= \alpha + \beta + \alpha \beta$

$= \frac{1}{3} - 2$

$= \frac{ 1 - 6}{3}$

$= \frac{ -5}{3}\: --(3)$

$iv ) Product\: of \: the \: zeroes$

$=( \alpha + \beta) (\alpha \beta)$

$= \frac{1}{3} \times 2$

$= \frac{2}{3}\: --(4)$

$\pink{ Form \: of \: Quadratic \: polynomial\:is: }$

$= k[ x^{2} - ( Sum \: of \: the \: zeroes)x+product \: of \: the \: zeroes ]$

$= k[ x^{2} - \frac{ -5}{3} x + \frac{2}{3}]$

$If \: k = 3 \: then$

$= 3x^{2} + 5x + 2$

Therefore.,

$\red{ Required \: polynomial : }$

$\green { = 3x^{2} + 5x + 2}$

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