Find solutions to your problems with the help of IDNLearn.com's expert community. Get step-by-step guidance for all your technical questions from our dedicated community members.
Sagot :
Answer:
f(x) = 2(x + 3)(x - 6)
Step-by-step explanation:
The possible values of [tex]x[/tex] for [tex]2\cdot x^{2}+6\cdot x = 36[/tex] are [tex]x_{1} = 3[/tex] and [tex]x_{2} = -6[/tex].
The expression [tex]2\cdot x^{2}+6\cdot x = 36[/tex] is equivalent to the expression [tex]2\cdot x^{2}+6\cdot x -36 = 0[/tex], which represents a second order polynomial, that is, a polynomial of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where [tex]a,\,b,\,c[/tex] are coefficients.
The possible values of x represents all possible roots of x, which are found analytically by the quadratic formula:
[tex]x = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (2)
If we know that [tex]a = 2[/tex], [tex]b = 6[/tex] and [tex]c = -36[/tex], then all possible values of [tex]x[/tex] are, respectively:
[tex]x_{1} = 3[/tex], [tex]x_{2} = -6[/tex]
The possible values of [tex]x[/tex] for [tex]2\cdot x^{2}+6\cdot x = 36[/tex] are [tex]x_{1} = 3[/tex] and [tex]x_{2} = -6[/tex].
We kindly invite to check this question on second order polynomials: https://brainly.com/question/24356198
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.