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You are given the function f(x)=x^3-x^2-7x+3, and that x=3 is a root of f(x)=0. Find the exact values of the other 2 roots. (6 marks)

First step is to realise that as x=3 is a root of f(x)=0, then we can use (x-3) as a factor of f(x). A really good method to use to find what (fx)/(x-3) gives is Synthetic Division. Using this method we then...
DH
Answered by David H. • Maths tutor
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How do you find the point or points of intersection of a straight line and a circle?

Given the equation of the straight line is: x+y=9 and the equation of the circle is: (x-2) 2 +(y-3) 2 =16 , find the point or points of intersection? The equation x+y=9 can be rearranged to make x=9-y. This ...
EC
Answered by Edward C. • Maths tutor
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Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)

Start the integration by parts process |udv = uv - |vdu u = (ln x) 2 dv = x 7 dx du = 2(ln x)/x dx v = 1/8 x 8 = 1/8 x 8 (ln x) 2 - | 1/4(ln x)x 7 dx = 1/8 x 8 (ln x) 2 -1/4 | x 7 (ln x) dx Repeat the integr...
RD
Answered by Rowan D. • Maths tutor
8586 Views

In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding ter...
SW
Answered by Sam W. • Maths tutor
6468 Views

The quadratic equation (k+1)x^2+12x+(k-4)=0 has real roots. (a) Show that k^2-3k-40<=0. (b) Hence find the possible values of k.

(a) There is a quadratic equation which should e solved using the delta andthe roots formulas. delta=a 2 -4ab delta=144-4(k+1)(k-4) delta=-4k 2 +12k+160 Because the problem tells us that the roots are real, ...
AB
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