Question

It is known that x1 and x2 are roots of the equation x2−8x+k=0, where 3x1+4x2=29. Find k.

Answer 1

Answer:

The answer to your question is   k = -3233

Step-by-step explanation:

Data

x₁, x₂ are the roots

Equation l      x² - 8x + k = 0

Equation ll     3x₁ + 4x₂ = 29

k = ?

Process

1.- Write another equation

                     x₁ + x₂ = - 8

2.- Solve the system of equations by elimination

                      3x₁ + 4x₂ = 29          Equation l

                        x₁ +   x₂ = -8            Equation ll

-Multiply equation ll by -3

                      3x₁  + 4x₂ = 29

                    -3x₁   - 3x₂ = 24

                       0    + x₂ = 53

-Find x₁

                       x₁ + 53 = -8

                       x₁ = -8 - 53

                       x₁ = -61

2.- Find k

                      (x₁)(x₂) = k

                      (53)(-61) = k

                      k = -3233