Question

Find the sum and product of the zeroes of the polynomial p(x) 2x^3 - 5x^2 - 14x +8

Answer 1

The sum and  product of the zeroes of the polynomial are 2.5 and -4 respectively.

Step-by-step explanation:

The given polynomial

$p(x)=2x^3-5x^2-14x+8$

If a three degree polynomial is $f(x)=ax^3+bx^2+cx+d$, then

Sum of zeroes = -b/a

Product  of zeroes = -d/a

In the given polynomial a=2, b=-5, c=-14 and d=8.

Sum of zeroes = -(-5)/(2) = 2.5

Product  of zeroes = -(8)/(2) = -4

Therefore, the sum and  product of the zeroes of the polynomial are 2.5 and -4 respectively.

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Answer 2

Answer:

$Sum \: of \: the \: zeroes = \frac{5}{2}$

$Product \:of \:the \: zeroes = -4$

Step-by-step explanation:

$Given \: p(x) = 2x^{3} - 5x^{2} -14x + 8$

$Compare \: p(x) , \: with \: ax^{3}+bx^{2}+cx+d\\we \:get$

$a = 2 , \: b = -5 ,\: c = -14 , \: d = 8$

$Sum \: of \: the \: zeroes = \frac{-b}{a} \\= \frac{-(-5)}{2}\\= \frac{5}{2}$

$Product \:of \:the \: zeroes = \frac{-d}{a}\\= \frac{-8}{2}\\= -4$

Therefore.,

$Sum \: of \: the \: zeroes = \frac{5}{2}$

$Product \:of \:the \: zeroes = -4$

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