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:

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