Please explain in detail.
find the value of 1/α + 1/β – 2αβ, when quadratic polynomial is f(x) = x2 – 5x + 4.
class 10th rd Sharma mathematics chapter 2nd polynomials.
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3. If α and β are the zeros of the quadratic polynomial f(x) = x2 – 5x + 4, find the value of 1/α + 1/β – 2αβ.
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Solution:
From the question, it’s given that
α and β are the roots of the quadratic polynomial f(x) where a = 1, b = -5 and c = 4
So, we can find
Sum of the roots = α+β = -b/a = – (-5)/1 = 5
Product of the roots = αβ = c/a = 4/1 = 4
To find, 1/α +1/β – 2αβ
⇒ [(α +β)/ αβ] – 2αβ
⇒ (5)/ 4 – 2(4) = 5/4 – 8 = -27/ 4