Math CentralQuandaries & Queries


Question from Rebecca, a student:

Determine the product of the roots of the equation
(x-1)(x-2) + (x-2)(x-5)=0

Hi Rebecca,

If you look at my response to Katelyn you will se that when you write a quadratic function in the form x2 + bx + c the product of the roots is the constant term c. What is the constant term in your expression?



Hi Rebecca.

You have to multiply it out, collect like terms, then factor it to find the roots. Multiply the roots together at the end to come up with the answer to the question.

For example, find the product of the roots of (a - 2)(a + 5) + (a + 1)(a - 2) = 0.

Multiply it out: a^2 + 3a - 10 + a^2 - a - 2 = 0.

Collect like terms: 2a^2 + 2a - 12 = 0.

Factor it: 2(a - 2)(a + 3) = 0.

The roots are 2 and -3, so the answer is -6.

Now try your question similarly.

Stephen La Rocque.

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