Question

Find the zeroes of the polynomial x^2+1/6x-2 and verify the realtion between the coefficient and zeroes of the polynom

Answer 1

Let f(x) = x2 + 1/6x - 2

Here a = 1, b = 1/6 and c = -2

x2 + 1/6x - 2 = 0

Multiplying by 6 throughout, we have

6x2 + x - 12 = 0

6x2 + 9x - 8x - 12 = 0

3x(2x + 3) - 4(2x + 3) = 0

(2x + 3)(3x - 4) = 0

2x + 3 = 0 or 3x - 4 = 0

x = -3/2 or x = 4/3

Sum of roots = -3/2 + 4/3 = -1/6

-b/a = -1/6/1 = -1/6

So, Sum of roots = -b/a

Product of roots = -3/2*4/3 = -2

c/a = -2/1 = -2

So, Product of roots = c/a