What is root? 30pts

All quadratic equations should have two roots. The general form is like this.

For example, ax^2 + bx +c=0
The two roots are
x =[ -b +(b^2-4ac)^0.5 ]/ 2a
and
x =[ -b -(b^2-4ac)^0.5 ]/ 2a

There is a square root here and we have to be careful of the term (b^2-4ac). There are 3 scenarios

a. If this term is positive (>0), then its square root will be a real number.
Then you will have TWO real roots as above

b. If this term is zero, then its square root is zero. Then you will have two equal roots. ie. -b/2a In this special case, you can say that there is one single real root. e.g. (x-1)^2=0 In principle, there are two real roots and they are both 1. So you can say that this equation has only one real root.

c. If this term is negative (<0), its square root will be a compex number (non-real). Then you will have two non-real roots.

So in your example as
Find the values of k if each of the following quadratic equations has a double real root.

It simply asks you to find the k value when b2-4ac>0 because only when b2-4ac>0, then you will have two real roots.

In summary, root is a general term as the answer to the quadratic equation. It can be a real number or a non-real number. Non-real number is also called complex number.

hi~

double root just mean a equation which have 2 root ,but they have the same value.

yes, when you find the value of x, the anw. is called as 'root'

x(3x+4)=(x+1)(x-2)

expand, then put all the object in left hand side, then put the formula into it.

x =[ -b +(b^2-4ac)^0.5 ]/ 2a
or

x =[ -b -(b^2-4ac)^0.5 ]/ 2a