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x 2 +5x+4=0 x 2 -5x+4=0 find the real roots to the given equation

x2+5x+4=0
x2-5x+4=0
find the real roots to the given equation

Grade:12th pass

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Using quadratic formula the roots for the first equation are -4,-1

and for the next equation, the roots are 4,1

Regards
Vikas TU
14149 Points
4 years ago
Dear student
a and b are the roots of x^2–5x+4=0
a+b=5……………………..(1)
a.b=4…………………………(2)
Divide eq.(1) by eq.(2)
(a+b)/a.b=5/4
or 1/b+1/a=5/4………………….(3)
On reversing eq.(2) both sides
or 1/a.b=1/4 or (1/a).(1/b)=1/4…………….(4)
put (1/b)=(5/4-1/a) from eq.(3)
(1/a).(5/4–1/a)=1/4
5/4a-1/a^2=1/4
1/a^2–5/4a+1/4=0
1/a^2–1/a-1/4a+1/4=0
1/a(1/a-1)-1/4(1/a-1)=0
(1/a-1)(1/a-1/4)=0
1/a= 1 , 1/4 ,
but 1/b=(5/4–1/a)
1/b=5/4–1 ,5/4–1/4
Good Luck 

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