00:01
This problem, we are required to calculate the x values for the intersection of f of x that has the value x squared plus x.
00:08
And again, we have g of x.
00:10
So that has the value minus 3x square.
00:13
And then here it will be plus 4x plus 2.
00:16
So with this value, what will happen? if we have to find out the value of intersection of these two functions, then we must find the value of x coming out of this equation.
00:26
So, if we put these two equations equals to one another, then the value of x, what we will get from this particular equation will fetch us the value for their intersection.
00:37
So, if we plug in the values now, that will be equals to x squared plus x equals minus 3x square plus 4x plus 2.
00:45
So if solved, our final equation will look like 4x square minus 4x square minus 4x square minus 3x minus 2.
00:55
And that is equal to 0.
00:57
So, what next will happen? d will be equals to b square minus 4 ac.
01:01
D is what? determinant of this quadratic equation.
01:04
So it will be equals to b square minus 4 ac for the general quadratic equation of a x square plus bx plus c.
01:10
So this value is going to be 9 minus 4 multiplied 4 multiplied minus of 2.
01:17
So with this value, what will happen? we can write, we can see that the value is coming out to be 41.
01:24
So if d.
01:25
Value is 41 that means it is greater than 0 and if it is greater than 0 that means that there will be 2 x values and those can we find out by the formula 3 plus under root of 41 and in the denominator we will be having 8 so how did we write this formula so we how did we write this value we write this value with the formula that says minus b plus under root of d over 2a and where does this b and a come from? b and a came from the equation, general equation of quadratic equation, which has the form this.
02:02
So we are taking this value of b and a from this particular equation.
02:07
So let us see how we can do now.
02:10
We can write x will be equals to again 3 plus, sorry, 3 minus now because we have already taken the x plus value.
02:20
So it will be 3 minus under root of 41 over 8.
02:25
And this is the answer for the first part.
02:27
These two values are the answer for the first part.
02:30
So we are required to put them inside the box, isn't it? so that will be like highlighting the answers.
02:36
So what formula have we used here? we have used the formula minus of b minus under root of d over 2a.
02:44
So my d looks somewhat cursive.
02:47
So we can just change this one into normal d that looks like this...