Question

Find the sum and product of zeroes of the polynomial 3x 2 -5x+6

Answer 1

we have to find sum and product of zeroes of the given polynomial 3x² - 5x + 6.

we know, for general form of quadratic polynomial, ax² + bx + c

• sum of zeroes = - coefficient of x/coefficient of x² = -b/a
• sum of zeroes = - coefficient of x/coefficient of x² = -b/a product of zeroes = constant/coefficient of x² = c/a

on comparing 3x² - 5x + 6 with ax² + bx + c we get, a = 3, b = -5 and c = 6

so, sum of zeroes = -b/a = -(-5)/3 = 5/3

product of zeroes = c/a = (6)/3 = 2

hence, sum of zeroes = 5/3

and product of zeroes = 2

Answer 2

Answer:

$sum\:of\:the \: zeroes=\frac{5}{3}\\product \:of\: zeroes = 2$

Step-by-step explanation:

$Let\:us\: assume \:\alpha\\and\:\beta \:are \: zeroes\:of\\given\: polynomial\:3x^{2}-5x+6.\\compare\:this \:with\\ax^{2}+bx+c,\:we\:get$

$a=3,\:b=-5,\:c=6$

$Now,\\sum\:of\:the \: zeroes\\=\frac{-b}{a}$$\implies \alpha+\beta=\frac{-(-5)}{3}\\=\frac{5}{3}$

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

$\implies \alpha\beta=\frac{6}{3}\\=2$

Therefore,

$sum\:of\:the \: zeroes=\frac{5}{3}\\product \:of\: zeroes = 2$

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