help please (1 Viewer)

[Smil3s]

a)prove that p(x) 1/4x^4- 1/3x^3-2x^2+4x+c has no real roots if c>28/3

b)explain why the largest zero of p(x) is greater than 2 if c=-2. find an approximation to 2dp for the largest zero of p(x) using one application of newtons method

 

[KingOfActing]

Consider the graph of the two functions and consider for what value of c they intersect for part a.

 

[Drongoski]

Another approach for (a):



You will find P''(-2) and P''(2) [min turning points] are positive and P''(1) is negative [max turning point]. Therefore graph is W-shaped. Also the turning point at x = -2 is lower (= c - 28/3) than the turning point at x = 2. So if c > 28/3, the whole W-shaped graph is above the x-axis and therefore P(x) will not attain the value '0' and so the equation will have no roots.

 

[integral95]

a)prove that p(x) 1/4x^4- 1/3x^3-2x^2+4x+c has no real roots if c>28/3

b)explain why the largest zero of p(x) is greater than 2 if c=-2. find an approximation to 2dp for the largest zero of p(x) using one application of newtons method

For the 2nd question,for c = -2, P(x) is always increasing for x>2 and P(2) is negative while P(3) is positive, so the root must exist between that interval.