Question

For what values of k, the zeroes of the polynomial x^2+kx+12 will differ by 1.

Answer 1

Answer:

given p(x) = x² + Kx + 12

a - b = 1

to find k

a×b = c/a

c = 12 and a = 1

therefore ab = 12

now let's use an identity to find the sum of zeros

(a + b)² - (a - b)² = 4 ab

=> (a + b)² = 4ab + (a - b)²

=> (a + b)² = 4×12 + (1)²

=> (a + b)² = 48 + 1

=> (a + b)² = 49

=> (a + b) = √49 = 7

- b/a = - k/1 = 7

=> k = -7