Question

If α and β are the zeroes of the polynomial ax²+bx+c, find the value of α²+β².

Answer 1

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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Answer 2

Answer:

b²-2ac/a²

Step-by-step explanation:

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