Question

Given that x²-kx+16 is aperfect square,find the value of k hence solve the equation
x²+kx+16=0

Answer 1

x² - kx + 16 is a perfect square. So k is equal to the double of square root of 16.

 

∴ k = 2√16

k = 2 × (± 4)

k = '± 8'

 

So there are two equations: x² + 8x + 16 and x² - 8x + 16.

The roots of these equations are '-4' and '4' respectively.

x² + 8x + 16 = (x + 4)²    ;     x = -4

x² - 8x + 16 = (x - 4)²    ;     x = 4

Hope this helps. Thank you. ;-))