We need to find two numbers p p p and q q q such that their product is −350-350−350 and their sum is −3-3−3. These numbers will be used to factor the quadratic equation w2−3w−350=0 w^2 - 3w - 350 = 0 w2−3w−350=0.
The factor pairs of −350-350−350 are:
We need to find the pair where the sum p+q=−3 p + q = -3 p+q=−3.
Checking the pairs:
None of these pairs satisfy the condition p+q=−3 p + q = -3 p+q=−3. Let's check the remaining pairs:
It seems there was a mistake in the initial list. Let's correct it:
This pair satisfies both conditions: p⋅q=−350 p \cdot q = -350 p⋅q=−350 and p+q=−3 p + q = -3 p+q=−3.
The correct factors are p=17 p = 17 p=17 and q=−20 q = -20 q=−20.
pqp+q10−35−25−10352550−743−507−4317−20−3 \begin{array}{|c|c|c|} \hline \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{p + q} \\ \hline 10 & -35 & -25 \\ \hline -10 & 35 & 25 \\ \hline 50 & -7 & 43 \\ \hline -50 & 7 & -43 \\ \hline 17 & -20 & -3 \\ \hline \end{array} p10−1050−5017q−3535−77−20p+q−252543−43−3
p=17, q=−20\boxed{p = 17, \, q = -20}p=17,q=−20
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