I really need some help for this problems because I have been confuse of this problems since the start and now the Examination is coming near and this is going to be added, I really will appreciate some help in this questions:
---find the value of k so that the equation will have equal roots.
Find the discriminant
To have equal roots the discriminant must equal 0, so
To check, we substitute for in
Multiply through by 12 to clear of fractions:
;
;
;
So the roots are equal.
-----------------------------------
---find the value of k so that the equation will have one roots numerically equal but opposite in sign
Then it will have to be true that we also get zero when we
substitute for :
And since we started with
We can set the left sides equal:
Divide thru by 2
Factor out x
;
So the value of k that will cause the
roots to be numerically equal but opposite
in sign.
Check by substituting -5 for k and solve:
and are numerically
equal but opposite in sign.
--what should be the range of the value of k so that the equation
will have real and unequal roots.
That is when the discriminant is positive
Find the discriminant
"Positive" means the same as "greater than 0"
So we set
Divide through by 9
Since is never negative the left side will always
positive no matter what value of k we use, so all values of
k will yield real and unequal roots.
So
---what should be the value of k so that the equation
will have equal roots?
Find the discriminant
To have equal roots the discriminant must equal 0, so
Divide thru by 4
Using the ,
Using the ,
Edwin