If α and β are the zeroes of the polynomial ax²+bx+c, find the value of α²+β².
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Answered by
5
Answer:
Given:
alpha and beta are the zeroes of polynomial ax² + bx + c
To find:
alpha²+ beta²
Pre - requisite Knowledge:
If α and β are the zeros,then,
α + β = -b/a
α * β = c/a
a² + b² = (a+b)² - 2ab
Solving Question:
We are given the polynomial and are asked to find the value of alpha square + beta square , we could find it by substituting the values in above equations.
Solution:
a² + b² = (a+b)² - 2ab
⇒ α² + β ²=(α + β )² -2αβ
and
α + β = -b/a
α * β = c/a
substitute the values,
⇒ α² + β²= ( -b/a )² -2(c/a)
or, α² + β²= b²/a² - 2c/a
or, α² + β²= ( b² - 2ac )/ a²
∴ The value of α² + β² is ( b² - 2ac )/ a²
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Answered by
3
Answer:
b²-2ac/a²
Step-by-step explanation:
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