Example-7. Find the roots of 4x2 + 3x + 5 = 0 by the method of completing the square.

Solution : Given 4x2 + 3x + 5 = 0

x2 + 3/4 x +5/4 = 0

x2 + 3/4x = - 5/2

x2 + 3/4x + (3/8)2 =-5/ 4 +(3/8)2

(x + 3/8)2 = - 5/4 + 9/64

(x + 3/8)2= - 71/64 < 0

But (x+3/8)² cannot be negative for any real value of x (Why?). So, there is no real value of x satisfying the given equation. Therefore, the given equation has no real roots.

Do This

Solve the equations by completing the square

i)x2 - 10x + 9 = 0     ii) x2 - 5x + 5 = 0      iii)x2 = 7x - 6 = 0


We have solved several examples with the use of the method of ‘completing the square.’

Now, let us apply this method in standard form of quadratic equation ax 2+bx+c=0 (a not equal to 0).

Step 1 : Dividing the equation by ‘a’ we get

x2 + b/ax + c/a = 0

Step 2 : x2 + b/ax = -c/a



pg no:117

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