Question

If a,b are the zeroes of f(x) =x2 + x+ 1,then find 1/a +1/b

Answer 1

Hey there!

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f (x) = x^2 + x + 1

Where, a = 1 , b = 1 , c =1

One zero = a
Second zero = b

Sum of zeroes ( a + b ) = - b/a = -1 / 1 = -1

Product of zeroes ( a × b ) = c/a = 1 / 1 = 1

We have to find value of , 1 / a + 1 / b
Taking LCM

= a + b / ab

Keeping the values now,

= -1 / 1
= -1

Thus, 1 / a + 1 / b = -1

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Hope it helps...!!!

Answer 2

Heya!!

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According to root's or zeroes concept of quadratic equation..

If a and b are zeroes of polynomial x^2 + x+1 (form of px^2 + qx+c) then..

Since A/Q..

p=1, q= 1 and c = 1.

=) a+b = - q/p

=) a+b = - 1/1 = - 1

And

=) a*b = c/p

=) a*b = 1/1 = 1

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To find : 1/a + 1/b :

Take lcm of a and b = ab

= (b+a) /ab

Put value of a+b and ab.

= - 1/1

= - 1

Hope it helps u :)