Question

if m,n are the zeros of the polynomial bx^2 +ax+c,then the value of m^2+n^2

Answer 1

Concept used :-

The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

Solution :-

Given Polynomial = bx² + ax + c

where,

→ a = b

→ b = a

→ c = c

So,

→ sum of zeros = (m + n) = (-b/a) = (-a/b) ----- Eqn.(1)

→ Product of zeros = m * n = c/a = (c/b) ------ Eqn.(2)

now, using a² + b² = (a + b)² - 2ab we get,

→ m² + n² = (m + n)² - 2mn

→ m² + n² = (-a/b)² - 2(c/b)

→ m² + n² = a²/b² - 2c/b

→ m² + n² = (a² - 2bc) / (b²) (Ans.)