Question

Find the roots of quadratic equation x^2 + 4x + 3 = 0 by " Comparing square method ".​

Answer 1

Step-by-step explanation:

Step 1 :

In the given quadratic equation ax2 + bx + c = 0, divide the complete equation by a (coefficient of x2).

If the coefficient of x2 is 1 (a = 1), the above process is not required.

Step 2 :

Move the number term (constant) to the right side of the equation.

Step 3 :

In the result of step 2, write the "x" term as a multiple of 2.

Examples :

6x should be written as 2(3)(x).

5x should be written as 2(x)(5/2).

Step 4 :

The result of step 3 will be in the form of

x2 + 2(x)y = k

Step 4 :

Now add y2 to each side to complete the square on the left side of the equation.

Then,

x2 + 2(x)y + y2 = k + y2

Step 5 :

In the result of step 4, if we use the algebraic identity

(a + b)2 = a2 + 2ab + b2

on the left side of the equation, we get

(x + y)2 = k + y2

Step 6 :

Solve (x + y)2 = k + y2 for x by taking square root on both sides.