Question

If alpha and beta are the zeroes of the quadratic equation f(x)=x^2-5x+4.find the value of 1/alpha + 1/beta - 2alpha×beta

Answer 1

Heya friend (^_^)

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

Hope this helps you

Answer 2

Step-by-step explanation:

α and β are the roots of the quadratic polynomial

f(x) where a = 1, b = -5 and c = 4

Sum of the roots = α + β = −b/a = – (−5)/1= 5

Product of the roots = αβ = c/a = 4/1= 4

1/α+1/β–2αβ⇒

[(α+β)αβ]– 2αβ ⇒

(−5)4(−5)4 – 2(4)

= −27/4

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