"If f(x)=kx^2+8x+k-6 determine the values of k that will give f(x) two zeroes."
Please show me how to do this, as well as answer it. It is very important and any help is great. Thanks.
Hello,
Think "discriminant", in .
If , there is no zero within the real numbers.
If , there is one zero.
If , there are 2 zeroes.
No, there are the values where (x+2)(x-8)<0, so that will be sets of values.
I'll give you a hint : a product of two factors is negative if and only if the two are of different sign.
This means that you have to solve two things :
- x+2>0 AND x-8<0
- x+2<0 AND x-8>0
One of the situation will not be possible
You can do it in two ways
The one I tried to describe with solving k+2>0 etc...
And another one, which is simpler, that's why I changed the method :
The roots are -2 and 8.
I don't know if you have learnt that if a polynomial has roots and (and ), then we can have the sign of the polynomial :
- sign of a if
- opposit sign of a if
Here, a=1, what can you conclude ?
You have:
So we have the points and .
is positive so the part to the right of is positive, the part to the left of will also be positive.
We want the part smaller than .
Those numbers lie between and , but the two aforementioned numbers are not included.