Find the zeros of the following quadratic polynomials and verify the basic relationships between the zeros and the coefficients.

x² – 15

Let f(x) = x² – 15

Arranging equation in proper form.

Now, f(x) = x² + 0x – 15

To find out zeros of the given polynomial.

We put f(x) = 0

⇒ x² – 15 = 0

∴ x² – = 0

So, (x + )(x – ) = 0

When, (x + ) = 0

Then, x = – .

When. (x – ) = 0

Then, x =

⇒ Our zeros are α = – and β = .

⇒ sum of zeros = α + β = – +

⇒ sum of zeros = α + β = 0

⇒ Product of zeros = αβ = – = – 15

Now, Comparing f(x) = x² + 0x – 15 with standard equation ax² + bx + c.

We get, a = 1, b = 0 and c = – 15.

We can verify,

⇒ Sum of zeros =

i.e. α + β =

∴ α + β = 0

⇒ Product of zeros =

αβ =

Hence, relationship between zeros and coefficient is verified.