Question

If α and β are the zeros of the quadratic polynomial f(x)=x2-x+4 , then evaluate: 1/α+1/β−2αβ

Answer 1

Here is your answer

=x²-5x+4

=x²-x-4x+4

=x(x-1)-4(x-1)

=(x-4)(x-1)

x-4=0

x=4

α=4

x-1=0

x=1

β=1

THE ZEROES ARE 4 AND 1

=1/α+1/β-2αβ

=(1/4)+(1/1)-(2×4×1)

=(1/4)+1-8

=(1+4-32)/4

=(5-32)/4

=-27/4

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Answer 2

f(x) = x^2 - x + 4

When you apply the quadratic formula for getting the roots,

x = (-b + or - √b^2 - 4ac) / 2a

You get roots as (1+√13i) /2 and (1-√13i) /2. Where, i is complex number as in the given equation, discriminant is clearly negative. Now, consider the roots as alpha and beta and finally substitute.

So, the final answer is 1/7.

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