Hey guys......
Plz derive the quadratic formula......
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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=0ax2+bx+c=0
x2+bax+ca=0x2+bax+ca=0
x2+bax=−cax2+bax=−ca
x2+bax+b24a2=b24a2−cax2+bax+b24a2=b24a2−ca
(x+b2a)2=b2−4ac4a2(x+b2a)2=b2−4ac4a2
. x+b2a=±b2−4ac−−−−−−−√2ax+b2a=±b2−4ac2a
x=−b2a±b2−4ac−−−−−−−√2ax=−b2a±b2−4ac2a
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=0ax2+bx+c=0
x2+bax+ca=0x2+bax+ca=0
x2+bax=−cax2+bax=−ca
x2+bax+b24a2=b24a2−cax2+bax+b24a2=b24a2−ca
(x+b2a)2=b2−4ac4a2(x+b2a)2=b2−4ac4a2
. x+b2a=±b2−4ac−−−−−−−√2ax+b2a=±b2−4ac2a
x=−b2a±b2−4ac−−−−−−−√2ax=−b2a±b2−4ac2a
x=−b±b2−4ac−−−−−−−√2a
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General formula
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