jmc

Question

Let the roots of the polynomial x^2 + 7x - 2 be and . Evaluate ^2 + ^2.

Accepted Answer

We make use of the following fact:

"For a quadratic equation

a x^{2} + b x + c,

the sum of the roots is

- b / a

while the product of the roots is

c / a .

'' Hence,

α + β = - 7

and

α * β = - 2.

Now, we use the fact that

(α + β)^{2} - 2 α β = α^{2} + β^{2} .

Or,

7^{2} + 4 = α^{2} + β^{2} .

Thus the answer is

53 .