Fsc Part 1 Mathematics (Complete Solution)

Q17
Find roots of the following equations by using quadratic formula

15x2 + 2ax - a2 = 0

Solution

Comparing the given equation with ax2 + bx + c = 0, we get
a = 15, b = 2a, c = -a2

By Quardratic formula, we have
x =
-b ±
b2 - 4ac
2a
Putting the values of a, b, and c in the formula
x =
-2a ±
(2a)2 - 4(15)(-a2)
2(15)
x =
-2a ±
4a2 + 60a2
30
x =
-2a ±
64a2
30
x =
-2a ±
(8a)2
30
x =
-2a ± 8a
30
Either        
x =
-2a - 8a
30
        OR        
x =
-2a + 8a
30
x =
-10a
30
x =
6a
30
x = -
a
3
x =
a
5


Hence Solution set =
{
-
a
3
,    
a
5
}

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