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Find two solutions to the quadratic equation x^2 + 2x - 15 = 0

Firstly, we need to find two numbers that multiply together to make -15 and sum together to make +2. We try a few numbers and find that the solution is -3 and 5, as -3 x 5 = -15 and -3 + 5 = 2.Next you input...
JG
Answered by James G. • Maths tutor
4670 Views

Use the substitution u = cos 2x to find ∫(cos^2*(2x) *sin3 (2x)) dx

∫(cos 2 2x *sin 3 2x)dx u = cos2x - u =(du/dx) = -2sin2x - differentiate u dx = du/(-2sin(2x)) - dx = -1/2 ∫cos 2 2x * sin 2 2x du - sub in dx-1/2 ∫u 2 (1-u 2 )du - put in terms if u -1/2 [ u 3 /3 - u 5 /5 ]...
WB
Answered by Will B. • Maths tutor
8398 Views

Does the equation x^2 + 2x + 5 = 0 have any real roots?

This equation has no real roots, as when we test the equation with the formula b 2 - 4ac, we get 2 2 -4 1 5 = 4 - 20 = -16. As this is negative we can be assured that this equation has no real roots.
SB
Answered by Sami B. • Maths tutor
5999 Views

Find the gradient of the tangent and the normal to the curve f(x)= 4x^3 - 7x - 10 at the point (2, 8)

y = 4x 3 - 7x -10The gradient of the function at any point can be found using its derivative:dy/dx = 12x 2 - 7The gradient of the function, m 1 , at (2,8) is equal to the gradient of the tangent at that poin...
MP
Answered by Miss P. • Maths tutor
6078 Views

What is compound interest?

Interest is the return you get on savings or an investment. Normal interest is when you earn a fixed percentage amount per year on an initial amount. For example an interest rate of 5% on £100 would give you...
YA
Answered by Yasmin A. • Maths tutor
3572 Views