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As we are considering a quadratic equation, we are looking for two values of x that make the equation equal to 0. To factorise, first look to the constant term (the term without any x) to find 2 numbers that...

First bring all the x terms to one side by taking 5x from each side, this gives 2x-4=8. Now put all the number terms on the other side by adding 4 to each side, this gives 2x=12. We can now divide both sides...

To integrate (32/ x 3 + bx) over x we can integrate each part separately. This is because addition of two integrals is the same as integrating the total of the elements. So we integrate 32/x 3 first, see tha...

Answer: (X+5)(X+2)=0 X=-5 or -2 We first look for to numbers that multiply together to make 10 (1 and 10, 2 and 5 are the only pairs) We choose the pair which also adds together to the 2nd term, 7. We can th...

The discriminant for a quadratic polynomial of the form f(x) = ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is strictly greater than 2, the quadratic has 2 real distinct roots, i.e 2 unique x-val...