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(k+1)(k-5)=0

May 13th, 2015

k+1)(k-5)=0

=>k+1=0;or k-5=0

=>k=-1;k=5.

hence

Solve Quadratic Equation by Completing The Square

4.2  Solving  k2-4k-5 = 0 by Completing The Square .
Add   to both side of the equation :
k2-4k = 5

Now the clever bit: Take the coefficient of  k , which is  4 , divide by two, giving  2 , and finally square it giving  4

Add  4  to both sides of the equation :
On the right hand side we have :
5 +  4 or,  (5/1)+(4/1)
The common denominator of the two fractions is  1  Adding  (5/1)+(4/1)  gives  9/1
So adding to both sides we finally get :
k2-4k+4 = 9

Adding  4  has completed the left hand side into a perfect square :
k2-4k+4  =
(k-2) • (k-2) =
(k-2)2
Things which are equal to the same thing are also equal to one another. Since
k2-4k+4 = 9 and
k2-4k+4 = (k-2)2
then, according to the law of transitivity,
(k-2)2 = 9

We'll refer to this Equation as  Eq. #4.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of
(k-2)2   is
(k-2)2/2 =
(k-2)1 =
k-2

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:
k-2 = √ 9

Add   to both sides to obtain:
k = 2 + √ 9

Since a square root has two values, one positive and the other negative
k2 - 4k - 5 = 0
has two solutions:
k = 2 + √ 9
or
k = 2 - √ 9

4.3  Solving  k2-4k-5 = 0 by the Quadratic Formula .
According to the Quadratic Formula, k , the solution for  Ak2+Bk+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

- B ±  √ B2-4AC
k =  ————————
2A  In our case, A =  1
B =  -4
C =  -5 Accordingly, B2 - 4AC =
16 - (-20) =

4 ± √ 36
k = —————
2Can  √ 36 be simplified ?

Yes! The prime factorization of  36  is
2•2•3•3
To be able to remove something from under the radical, there have to be   instances of it (because we are taking a square i.e. second root).

36  = √ 2•2•3•3  =2•3•√ 1  =
± 6 • √ 1  =
± 6

So now we are looking at:
k = ( 4 ± 6) / 2

Two real solutions:

k =(4+√36)/2=2+3= 5.000

or:

k =(4-√36)/2=2-3= -1.000

1.  k = 5
2.  k = -1

May 13th, 2015

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May 13th, 2015
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May 13th, 2015
Dec 9th, 2016
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