explain the formula used.
find the value of 1/α+1/β–αβ, when quadratic polynomial is f(x)=x2 – x – 4
class 10th polynomials question of rd Sharma.
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If α and β are the zeros of the quadratic polynomial f(x)=x2 – x – 4, find the value of 1/α+1/β–αβ.
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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 = -1 and c = – 4
So, we can find
Sum of the roots = α+β = -b/a = – (-1)/1 = 1
Product of the roots = αβ = c/a = -4 /1 = – 4
To find, 1/α +1/β – αβ
⇒ [(α +β)/ αβ] – αβ
⇒ [(1)/ (-4)] – (-4) = -1/4 + 4 = 15/ 4