Question

if m and n are the roots of quadratic equation X square - 5 x + 3 is equal to zero then find the value of M + nwhole square + A minus n
whole square ​

Answer 1

Let us know the relation between roots and coefficients first:

We consider the following quadratic equation

ax^2 + bx + c = 0

If p, q be its roots, then

• p + q = - b/a
• pq = c/a

Now we proceed to solve the given problem:

The given equation is

x^2 - 5x + 3 = 0

The roots are m and n. Then

• m + n = - (- 5/1) = 5
• mn = 3/1 = 3

Therefore, (m + n)^2 + (m - n)^2

= (m + n)^2 + (m + n)^2 - 4mn

= 2 (m + n)^2 - 4mn

= 2 (5)^2 - 4 (3)

= 2 (25) - 4 (3)

= 50 - 12 = 38

∴ (m + n)^2 + (m - n)^2 = 38

Related problems:

1. Relationship between roots of a cubic equation - https://brainly.in/question/3185801
2. If alpha beta are the root of the qualification x square - 2 X - 1 = 0 find the value of Alpha square beta + beta square alpha - https://brainly.in/question/8613021