Question

Find the zeroes of the quadratic polynomial x

2
+ x−12 and verify the relationship between the zeroes
and the coefficients.

Answer 1

Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

Quadratic formula:

Therefore,

a = 2√3

b = 5

c = - 4√3

Substituting the values into the quadratic formula:

The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.