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Solving Quadratic equation by method of Completion of Square
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Solving Quadratic equation by method of Completion of Square
Example : Solve the quadratic equation
x2 - 7x - 5 = 0.
Solution : Comparing the given equation with ax2+ bx + c = 0, we find that
a=l,6 = -7 and c = -5.
Therefore, D = (-7)2 - 4 * 1 * (- 5)
= 49 + 20
= 69
> 0
Since D is positive, the equation has two roots given by
(7 + 69)/6, (7 - 69)/6
i.e. x = (7 + 69)/6, (7 - 69)/6 are the required solutions.
Example : Determine value (s) of p for which the quadratic equation
2x2 + px + 8 = 0 has real roots.
Solution : D = b2- 4ac
b2- 4 * 2 * 8
For the equation having real roots, D > 0,
i.e., p2-64>0 or p2 >64, i.e., p2 >82
This gives p>8 or p<-8.
[Note: p2-82 >0gives
(p + 8)(p - 8)>=0
(1)
(1) holds if (i) p + 8 > 0
and p - 8 > 0
i.e., p>-8 and p>8
These give p > 8.
or
(ii) p + 8 < 0 and p - 8
< 0
i.e., p<-8 and p<8
These give p < -8.
Therefore, required values of p are p > 8 or p
<-8
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