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# algebra 2

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Suppose r and s are the roots of the equation 3x^2 + 9x + 15 = 0. Find (r+1)(s+1)

Dec 29, 2022

#1
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By the quadratic formula, the roots are -1/2*i*(sqrt(11) +- 3i).  Plugging those in, we get (r + 1)(s + 1) = -6.

Dec 29, 2022
#2
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We want to find$$(r+1)(s+1) = rs + s + r + 1$$

From Vieta's, we know that $$rs = {c \over a} = {15 \over 3} = 5$$ and that $$r + s = -{b \over a} = -{9 \over 3} = -3$$

So, we have $$5 - 3 + 1= \color{brown}\boxed{3}$$

Dec 29, 2022