Questions

MUF0091 Mathematics Unit 1 - Semester 1, 2025

Multiple fill-in-the-blank

Question textGuidelines to answer the following question:Fill in the blanks with the correct answers. Do NOT use any spaces or brackets. For all numerical answers, give EXACT values (i.e. do not round your answers) unless instructed otherwise in the question. If using fractions, give answers as SIMPLIFIED fractions using the forward slash (e.g. 1/2 or 5/4). Use - for any negatives. _____________________________________________________________This question is worth 2 + 2 = 4 marks.The graph of [math: g(x)=ax3+bx2+16] g(x)=ax^3+bx^2+16 has both an x-intercept and a turning point at [math: x=2] . a. Use the given information to set up two simultaneous equations. Fill in the blanks.Answer 1 Question 5[input][math: a+b=−4] a+ b=-4 (1)Answer 2 Question 5[input][math: a+b=0] a+ b=0 (2) b. Solve the equations to find the values of [math: a] and [math: b] .[math: a=] Answer 3 Question 5[input] [math: b=] Answer 4 Question 5[input]

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The problem asks us to fill in two equations derived from the information g(x) = a x^3 + b x^2 + 16 with a turning point and an x-intercept at x = 2. To analyze this, consider the function and its derivative. First, compute the derivative: g'(x) = 3a x^2 + 2b x. Since x = 2 is a turning point, the derivative must be zero at x = 2. Plugging in x = 2 gives 3a(2^2) + 2b(2) = 0, which simplifies to 12a + 4b = 0. Dividing by 4 yields the equation 3a + b = 0. Second, use the inf......Login to view full explanation

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