Answer:
k = 15
Step-by-step explanation:
∵ x² - 8x + k = 0 ⇒ has two roots x1 and x2
∵ ax² + bx + c = 0 has two roots
∴ The sum of roots = -b/a and the product of them = c/a
∵ a = 1 , b = -8 and c = k
∴ x1 + x2 = -(-8)/1 = 8
∴ x1 + x2 = 8 ⇒ (1)
∵ 3x1 + 4x2 = 29 ⇒ (2)
Multiply (1) by -4
∴ -4x1 - 4x2 = -32 ⇒ (3)
Add (2) and (3)
∴ -x1 = -3
∴ x1 = 3
By substituting value of x1 in (1)
∴ 3 + x2 = 8
∴ x2 = 5
∴ The roots are 3 and 5
∴ c/a = 3 × 5 = 15 ⇒ (a = 1)
∴ c = 15
∴ k = 15
