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Find the values of k for which the equation (2k-3)x^2-kx+(k-1) has equal roots

We know that an equation has equal roots if the sqrt(b^2-4ac) term in the quadratic equation is equal to zero. Therefore using this information we can form an expression for k to be (-k)^2-4(2k-3)(k-1)=0. Fr...
EH
Answered by Eliott H. • Maths tutor
13867 Views

Earth is being added to a pile so that, when the height of the pile is h metres, its volume is V cubic metres, where V = (h6 + 16) 1 2 − 4.Find the value of dV/dh when h = 2.

As V=(h 6 +16) 1/2 -4 , the chain rule can be used to calculate dV/dh. dV/dh=3h 5 (h 6 +16) -1/2 h=2 can be substituted in to find the solution. 3 2 5 (2 6 +16) -1/2 =10.73
LK
Answered by Lewis K. • Maths tutor
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What are the roots of y=x^2+5x+6 ?

Roots = where line touches x-axis. Set equation equal to 0 as y=0 at the x-axis. Now we need to solve for the x values at which y=0. Quadratic is now 0=x^2+5x+6. Factorise quadratic: 0=(x+3)(x+2). Now you ca...
SW
Answered by Sam W. • Maths tutor
7869 Views

Differentiate f(x)= x^3 + x^(1/3)-2

f'(x)= 3x^2+1/3x^(-2/3) To differentiate you need to multiply the coefficant of the x dependent terms by the powers and then the power of x goes down by one. For example: differentiate f(x) = x^n. f'(x) = nx...
JR
Answered by Jathursa R. • Maths tutor
4205 Views

Integrate 10x(x^1/2 - 2)dx

First, expand the brackets. This will give us 10x^3/2 - 20x. Now to integrate this expression we have to increase the power of each term by one and then divide them by the number which becomes the new power....
GS
Answered by Giorgia S. • Maths tutor
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