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The roots of y^2 - 5y - 11 = 0 are a and b. Find (a + 3)(b + 3).

 Feb 12, 2022
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By vieta, the sum of the roots (a+b) is 5 (the b term * -1) and the product of the roots (ab) is -11 (the c term).

To clarify: \(a + b = 5\), and \(ab = -11\)

Then, when we open up the parenthesis for (a+3)(b+3), we get ab + 3b + 3a + 9. We can simplify that new expression to:

\(-11 + 3(5) + 9\)

 

So, (a + 3)(b + 3) = 13.

 

smiley

 Feb 12, 2022

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