Question

if a and B Are zeroes of the polynomial x² +bx+c then evaluate 1/a+1/B
(a= alpha ; B=beta)​

Answer 1

Answer:

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Answer 2

Given:

x² + bx + c

à (alpha) and ß(beta) are zeroes of the polynomial.

To find:

1/ à + 1/ ß

Solution:

x² + bx + c

on Comparing with standard equation we get,

a = 1

b = b

c = c

Sum of zeroes = - (coefficientof x / coefficient of x²)

= - ( b/a)

à + ß = -b/1

Product of zeroes = constant term / coefficient of x²

= c / a

àß = c/1

Now,

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ substituting \: values \: \\ \\ = > \frac{ - b}{c}$

Hence, 1/ à + 1/ ß = -b/c

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