✔ 最佳答案
1.If the expression x^2+(1-q)+2q is greater than 2 for all real values of x, find the range of values of q.
why the solution is
[(1-q)^2]-4(2q-2)<0
(q-1)(q-9)<0
therefore, 1<q<9
instead of (q-1)(q-9)>0???x is real so why isn't the discriminant >0?
It is because if D>=0, then it means that the quadratic equation x^2+(1-q)+2q-2 =0 has real roots. This implies that for x^2+(1-q)+2q, not all real values of x are greater than 2
2. Show that -1+2x-3x^2 is always negative for all real values of x.
Solution is like this:
a<0 and
D=2^2-4(-3)(-1)
=-8
<0
therefore the expression is negative for all real values of x.
The question states that x are real values, but why the discriminant
turns out to be negative, which means that there is no real x???
It is because D<0 means that the quadratic equation -1+2x-3x^2 does not pass through the x-axis.Also, the leading coefficient is -3 indicates that the curve is downside. So, -1+2x-3x^2 should be always less than 0
3.solve
{y=2x^2-4x+5..1
{y=mx...2
what is the meaning of substituting the linear equation into the
quadratic one? And why is if the line touches the parabola, then
the discriminant of the combined equation =0? Please show the
explanation by a graph if possible.
It is because if (x,y) is the intersection point of the line and the parabola, then it should satisfies both equation. And if you want to solve x, the easiest method is to substitute y=2x^2-4x+5 into y=mx. Now, since the line touches the parabola, it means that there is only one intersection point (x,y). Change it into "algebra", this is equivalent to say that the discriminant of the combined equation = 0
2008-12-21 22:26:59 補充：
Oh, do you means that x is real so why isn't the discriminant >0
2008-12-21 22:27:08 補充：
As you know that for quadratic equation ax^2+bx+c=0, there should have two roots. The purpose of the D is to determine whether the roots are real or complex.
2008-12-21 22:27:14 補充：
If D<0 then ax^2+bx+c does not have real roots (and real roots only). Of course for any quadratic polynomial ax^2+bx+c, you can substitute any real or complex numbers x into it and there is no relationship with D!!!
