Question

Answer plz very urgent

Prove that x= -b+/-(root). b^2-4ac/2a


If ax^2+bx+c=0

Proper answer want otherwise I report

Answer 1

Given  :

a x² + b x + c = 0

Multiply both sides by a :

a²x² + abx + ac = 0

= > a²x² + abx = - ac

Now abx = a × b/2 × x × 2 .

Now : a²x² + 2 a . b/2 = - ac

= > a²x² + 2 a. b/2 + b²/4 = b²/4 - ac

= > ( ax + b/2 )² = ( b² - 4 ac ) / 4

= > ax + b / 2 = ± √ ( b² - 4 ac ) / 2

= > ax = [ - b ± √ ( b² - 4 ac ) ] / 2

= > x = [ - b ± √ ( b² - 4 ac ) ] / 2a

Hence proved.

Answer 2

Answer:

Step-by-step explanation:

ax^2+bx+c = has equal roots.

We know that if roots are equal say x1 and x1 then we can write the equation as:

(x-x1)(x-x1) = 0 and ax^2+bx+c = 0 same equations.

So a(x-x1)(x-x1) = ax^2+bx+c must be an identity.

Expanding the left, we get:

ax^2 - 2ax1*x+ax1^2 = ax^2+bx+c. is an identity.

So we can equate the like terms on both sides.

-2ax1 = b ..(3)

ax1^2 = c....(4)

We eliminate x1 between (3) and (4).

(-2ax1)^2/ax1 = b^2/c

4a^2/a = b^2/c

4ac= b^2 . Or b^2-4ac = 0.