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Two questions on Algebra 2?
1. How do write a quadratic equation whose roots are k and -k in simplest form?
2. The roots of x² - 5x + c = 0 differ by 3
a. What are the roots of the equation
b. what is c?
Thanks.
2 Answers
- FazLv 71 decade agoFavorite Answer
Q1
a(x+k)(x-k) = 0
a(x² - k²) = 0
Q2
Quadratic form:
x² - (sum of roots)x + (product of roots) = 0
Let roots be a and (a-3). We know the sum of roots is 5 so:
a+(a-3) = 5, so a=4
c= 4(4-3) = 4
Roots are x=1 and x=4
Equation :
x² - 5x + 4 = 0
(x-4)(x-1) = 0
- 1 decade ago
1.
x=k ==> x-k=0....(i)
x=-k ==> x+k=0...(ii)
(i)*(ii),
(x-k)(x+k)=0
x²-k²=0
which is your answer.
2.
Let roots be a and a+3
>>>Method 1
x=a ==> x-a=0...........(i)
x=a+3 ==> x-a-3=0........(ii)
(i)*(ii),
(x-a)(x-a-3)=0
x²-ax-ax+a²-3x+3a=0
x²-(2a+3)+(a²+3a)=0
Comparing this with x²-5x+c=0,
2a+3=5 ==> a=1
a²+3a=c ==> c = 1²+3*1 = 4
a=1 , a+3=4
Roots are 1 and 4
c=4
which is your answer
>>>Method 2
Sum of roots=5
i.e. a+a+3=5 ==> a=1
a+3=4
Product of roots=c
i.e. a(a+3)=c ==> c = 1²+3*1 = 4
So roots are 1 and 4
c=4
Hope this helps...
