Question

roots of equation ax²+bx+c=0 are​

Answer 1

Answer:

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ax^2 + bx + c = 0

Divide the whole equation by a, where a does not equal 0.

x^2 + (b/a)x + (c/a) = 0

Complete the square on x^2 + (b/a)x

You would halve b/a to get b/2a, then square it to

get b^2/(4a^2)

(x^2 + (b/a)x + (b^2/(4a^2)) - (b^2/(4a^2)) + c/a = 0

(x + b/2a)^2 -b^2/4a^2 + 4c/(4a) - 0

(x + b/2a)^2 +(-b^2 + 4ac)/(4a^2) = 0

(x + b/2a)^2 = (b^2 - 4ac)/(4a^2)

x + b/2a = +/- sqrt (b^2 - 4ac)/(2a)

x = - b/2a +/- sqrt (b^2 - 4ac)/(2a)

Express this with a common denominator of (2a)

x = (-b +/- sqrt (b^2 - 4ac))/(2a)

This is how the quadratic equation was derived.

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