Question

write derivation of quardatic formula using completing the square method class 10th

Answer 1

Answer:

Step-by-step explanation:

The roots of a quadratic equation ax2 + bx + c = 0 is given by the quadratic formula

x=−b±b2−4ac−−−−−−−√2a

The derivation of this formula can be outlined as follows:

Divide both sides of the equation ax2 + bx + c = 0 by a.

Transpose the quantity c/a to the right side of the equation.

Complete the square by adding b2 / 4a2 to both sides of the equation.

Factor the left side and combine the right side.

Extract the square-root of both sides of the equation.

Solve for x by transporting the quantity b / 2a to the right side of the equation.

Combine the right side of the equation to get the quadratic formula.

See the derivation below.

Derivation of Quadratic Formula

ax2+bx+c=0

x2+bax+ca=0

x2+bax=−ca

x2+bax+b24a2=b24a2−ca

(x+b2a)2=b2−4ac4a2

x+b2a=±b2−4ac−−−−−−−√2a

x=−b2a±b2−4ac−−−−−−−√2a

x=−b±b2−4ac−−−−−−−√2a