Question

If x1 and x2 are the roots of the equation x^2 +5x-3=0, determine the value of x1^2 + x2^2. I know that I have to use vietas formula, but I am stuck :( any help would be appreciated

Answer 1

Answer:

31

Step-by-step explanation:

Given

x² + 5x - 3 = 0

with a = 1, b = 5, c= - 3 , then

sum of roots x₁ + x₂ = - $\frac{b}{a}$ = - $\frac{5}{1}$ = - 5

product of roots = $\frac{c}{a}$ = $\frac{-3}{1}$ = - 3

Now

(x₁ + x₂)² = x₁² + 2x₁x₂ + x₂² , that is

(- 5)² = x₁² + 2(- 3) + x₂²

25 = x₁² - 6 + x₂² ( add 6 to both sides ), then

x₁² + x₂² = 31