Question

If a and b are the zeros of the polynomial 2x^2-4x+5,then find the value of a^2+b^2

Answer 1

Good Afternoon.

For a general Quadratic polynomial say

F(y) = ay² + by + c

Alfa + Beta = -b/a

And

Alfa × Beta = c/a

Where Alfa and Beta are zeros of polynomial.

F(x) = 2x² - 4x + 5

a + b = 4/2 = 2

And

a×b = 5/2

a² + b² = ( a + b )² - 2ab

a² + b² = ( 2 )² - 2 ( 5/2 )

a² + b² = 4 - 5

a² + b² = -1

So, a² + b² = -1