Question

The sum of the two roots of a quadratic equation is 5 and their product is -6. What is the quadratic equation?

Answer 1

Suppose a and b are the roots of a quadratic equation, p(x). Then (one) form of p(x) is
p(x) = (x-a)(x-b)
= x^2 - (a+b)x + ab

Notice that a+b is the sum of the roots and ab is the product.

Can you now solve your problem?

Answer 2

Yes, even I thought of it quite differently.

Answer 3

\[x + y = 5\]

Answer 4

\[xy=-6\]

Answer 5

multiplying he first equation by y

Answer 6

\[xy + y^2 = 5y\]

Answer 7

so -6 + y^2 = 5y

Answer 8

Is that correct?

Answer 9

Yes, so rearranging:
y^2 - 5y - 6 = 0.

You can decide which method is shorter.

Answer 10

I think yours is better hehe.

Answer 11

Thank you

Answer 12

I did not know of the second method ... thanks!