Without solving the quadratic equation 2x^(2) -10x+12=0, find the sum of the squares of its roots, x_(1)^2 + x^(2)_(2)

Question

Without solving the quadratic equation
`2x^(2) -10x+12=0`, find the sum of the squares of its roots,
`x_(1)^2 + x^(2)_(2)`

Answer 1

13

Explanation:

Take out the common factor of 2 using the inverse of the distributive property.

2(x^2 - 5x + 6)

Now factor the trinomial

(x - 2)(x - 3)

And find the 2 roots.

x1 -2 = 0

x1 = 2

x2 - 3 = 0

x2 = 3

x1^2 + x2^2 = 2^2 + 3^2 = 4 + 9 = 13