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Factorize x^2 + 4x -5 and hence find the roots of the quadratic equation y = x^2 + 4x - 5.

First, identify the integer factors of the constant. In this case -5, has factors -1,5 and 1,-5. Now check to see if the sum of either pair is equal to the value of the coefficient of x. In this case, the va...
AW
Answered by Alexander W. • Maths tutor
8543 Views

How can do you factorize the equation x^2+6x+8

Here, we see that the term in x in the equation is 6, so we start by looking for a perfect square where the second term would be 6 : we get 6/2 = 3 so we try (x+3) 2. However, (x+3) 2 = x 2+ 6x + 9. We thus ...
MS
Answered by Marine S. • Maths tutor
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Differentiate with respect to x, x^2*e^(tan(x))

Use the product rule: d/dx(uv) = uv' + u'v, with u = x^2 and v = e^(tan(x)), so that u' = 2x and v' = sec^2(x) * e^(tan(x)), and so the answer is 2x * e^(tan(x)) + x^2 * sec^2(x) * e^(tan(x)) .
JH
Answered by Jakub H. • Maths tutor
5874 Views

Using partial fractions, find f(x) if f'(x)=5/(2x-1)(x-3)

First step: partial fractions 5/(2x-1)(x-3) 5=A(x-3)+B(2x-1) A=0 when x=3, so B=5/(2x3-1)=1 B=0 when x=1/2, so A=5/(0.5-3)=-2 So f'(x)=1/(x-3)-2/(2x-1) Second step: Integration f(x)= (integral)(1/(x-3))dx - ...
JF
Answered by Jasmin F. • Maths tutor
5709 Views

Calculate the gradient of this straight line

The gradient of a striaght line measures how much it changes when you move in one direction. For example when we move to the right in the x direction, the line goes down. The equation for finding the gradien...
TD
Answered by Tutor67677 D. • Maths tutor
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