if alpha and beta are the zeros of the polynomial X square + 7 X + 12 then find the value of 1/ alpha + 1/ beta - 2 alpha beta.
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Answered by
21
Answer:
Step-by-step explanation:
Given polynomial,
Also, it's zeroes are and .
Therefore, we have, sum of zeroes,
And, product of zeroes,
Now, we have to find the value of,
Further simplifying, we will get,
Substituting the respective values, we get,
Hence, the required value is
Answered by
50
Given polynomial:
x² + 7 x + 12
α and β are zeroes of polynomial x² + 7 x + 12
αβ = 12
The product of the roots is the constant term
α + β = -7
The sum of the roots is the coefficient of x term , negated.
1/α + 1/β - 2 αβ
= (α + β) / αβ - 2 αβ
= -7/12 - 2 * 12
=(-7/12) - 24/1
Taking LCM now,
→ (-7 - 24*12) / 12
→ (-7 - 288) / 12
→ (-295) / 12 (Ans).
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