Question

if alpha and beta are the zeros of the quadratic polynomial x^2+x+1 find the value of 1/alpha+1/beta

Answer 1

Step-by-step explanation:

X^2+X+1

A=1. B=1. C=1

ALPHA+BETA=-B/A

-1/1

ALPHA×BETA=C/A

1/1

1

1/ALPHA+1/BETA

BETA+ALPHA/ALPHA×BETA

-1/1

ANSWER=-1.

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Answer 2

Sum of the zeroes

alpha + beta = -b/a = -1/1 = -1

product of the zeroes

alpha × beta = c/a = 1/1= 1

now we have a quadratic polynomial ax^2+bx+c, whose zeroes are 1/alpha and 1/beta

1/alpha + 1/beta = -b/a

beta + alpha/alpha × beta = -b/a

-1/1 = -b/a

and 1/alpha × 1/beta = c/a

1/alpha × beta = c/a

1/1 = c/a

alpha + beta = -b/a = -1/1

alpha × beta = c/a = 1/1= 1

therefore, a = 1, b = -1, c = 1

therefore the polynomial is x^2-x+1