Question

find the roots of the quadratic equation axsquare + bx + c is equal to zero where a unequal to zero

Answer 1

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Answer 2

Hello,

when it is equal to 0 :
I.e.
$ax^{2} + bx + c = 0$
There are 2 methods.
1) Factorization
2) Formula


The roots are
1)
$\frac{( - b + \sqrt{(b^{2} - 4ac) } )}{2a}$
2)
$\frac{( - b - \sqrt{(b^{2} - 4ac) } )}{2a}$
When it is not equal to 0 :

Equate it to 0.
E.g.
4x² + 2x + 4 = 6
Transfer 6 to LHS,
i.e. => 4x² + 2x + 4 - 6= 6 - 6
=> 4x² + 2x +(-2) = 0
=> 4x² + 2x - 2 = 0.
And then factorize.
=> 4x² + 4x - 2x - 2 = 0.
=> 4x(x + 1) - 2(x + 1) = 0
=> (4x - 2)(x + 1) = 0
Therefore either 4x - 2 is 0 or x + 1 is 0
(Because 0 × x = 0.)

Therefore x = 1/2 or x = -1.
The roots are 1/2,-1.

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