Question

If the roots of a quadratic equation are m + n and m - n then the quadratic equation will be

Answer 1

Answer:

x² - 2mx + m²-n² = 0

Step-by-step explanation:

Let α and β be the roots of the equation

The quadratic equation is of form x² - (Sum of roots)x+ (Product of roots) = 0

α = m + n

β = m - n

Sum of roots = α+β = m +n +m - n = 2m

Product of roots = αβ = (m+n)(m-n) = m² - n².

Thus the quadratic equation is x² - (α+β)x + αβ = x² - 2mx + m² - n² = 0