Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
There are two possible answers:
t = 2/3 or t = -1/3
========================================================
Explanation:
The expression x+3 is the same as x-(-3). It is of the form x-k
Recall that by the remainder theorem, we know that p(x) is divisible by (x-k) if and only if p(k) = 0.
In this case, k = -3. Plug this into the p(x) function and we get
p(x) = t^2*x^3 - 3t*x + 6
p(-3) = t^2*(-3)^3 - 3t*(-3) + 6
p(-3) = -27t^2 + 9t + 6
Set that equal to 0
p(-3) = 0
-27t^2 + 9t + 6 = 0
-3(9t^2 - 3t - 2) = 0
9t^2 - 3t - 2 = 0
Now apply the quadratic formula to solve for t
[tex]t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \frac{-(-3)\pm\sqrt{(-3)^2-4(9)(-2)}}{2(9)}\\\\t = \frac{3\pm\sqrt{81}}{18}\\\\t = \frac{3\pm9}{18}\\\\t = \frac{3+9}{18}\ \text{ or } \ t = \frac{3-9}{18}\\\\t = \frac{12}{18}\ \text{ or } \ t = \frac{-6}{18}\\\\t = \frac{2}{3}\ \text{ or } \ t = -\frac{1}{3}\\\\[/tex]
We get two possible solutions for t.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
