lz54428
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

please help thats the answer but i dont know
how to get it

Please Help Thats The Answer But I Dont Knowhow To Get It class=

Sagot :

Here we have to find zeroes of the given function.

Let's start solving!

[tex]f(x) = x ^{3} + 9x ^{2} + 6x - 16[/tex]

  • To find x-intercept or zeroes, Substitute f(x) =0

[tex]0 = x ^{3} + 9x ^{2} + 6x - 16[/tex]

  • Move the expression to the left hand side and change its sign

[tex]0 - x ^{3} - 9x ^{2} - 6x + 16 = 0[/tex]

[tex] - x ^{3} + x ^{2} - 10x ^{2} + 10x - 16x + 16 = 0[/tex]

[tex] - x ^{2} (x - 1) - 10x(x - 1) - 16(x - 1) = 0[/tex]

[tex] - (x - 1) \times (x ^{2} + 10x + 16) = 0[/tex]

[tex] - (x - 1) \times (x ^{2} + 8x + 2x + 16) = 0[/tex]

[tex] - (x - 1) \times (x \times (x + 8) + 2(x + 8)) = 0[/tex]

[tex] - (x - 1) \times (x + 8) \times (x + 2) = 0[/tex]

[tex](x - 1)(x + 8)(x + 2) = 0[/tex]

[tex]x - 1 = 0 \\ x + 8 = 0 \\ x + 2 = 0[/tex]

[tex]x = 1 \\ x = - 8 \\ x = - 2[/tex]

[tex] x_{1} = 8, x_{2} = - 2, x_{3} = 1[/tex]

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.