Question

If alpha and beta are the zeroes of quadratic polynomial ax2+bx+c find the value of 1/alpha+1/beta

Answer 1

Answer:

-b/c

Step-by-step explanation:

ax^2 + bx + c

now,

sum of zeroes=α+β= - b/a

product of zeroes = αβ

so 1/α + 1/β = (α+β) /αβ

= (-b/a) /(c/a)

= - b/c

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Answer 2

1/α + 1/β = -b/c if alpha (α) and beta (β) are the zeroes of quadratic polynomial ax²+bx+c

Quadratic polynomial is of the form ax²+bx+c   where a  , b and c are real also  a≠0.

Sum of zeroes of ax²+bx+c is given by  -b/a

Product of zeroes of ax²+bx+c is given by c/a

alpha (α) and beta (β) are the zeroes of quadratic polynomial ax²+bx+c hence

α + β = -b/a

αβ = c/a

1/α + 1/β

= (β + α)/αβ

= (α + β)/αβ

Substitute the values of α + β  and αβ

= (-b/a)/(c/a)

= -b/c

Hence 1/α + 1/β = -b/c