Question

If alpha and beta are the zeroes of polynomial ax2 + bx + c. Then find alpha2+ beta2

Answer 1

here is your answer

p(x)= ax^2+bx+c

alpha+beta = -b÷a

=-1÷1=-1

alpha× beta = c÷a

=1÷1=1

Now

alpha^2+beta^2 = (alpha + beta)^2 -2×alpha×beta

=(-1)^2+2×1

=1+2

=3

solved

Answer 2

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