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

(note it is not 3x^1 and 4x^2 it is 3x sub 1 and 4x sub 2)

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