Question

Obtain the roots of the general quadratic equation ax2 + bx + c = 0 (a ≠ 0, a, b, c are constants.)​

Answer 1

Answer:

For a quadratic equation ax2 + bx + c = 0, The roots are calculated using the formula,

x = (-b ± √ (b² - 4ac) )/2a.

Discriminant is, D = b2 - 4ac.

If D > 0, then the equation has two real and distinct roots.

or

ax2 + bx + c = 0

ax2 + bx=-c

now divide both sides by a

(ax2+bx)/a=-c/a

x2+(b/a)x=-c/a

now add both sides b^2/4a^2

x2+(b/a)x+b^2/4a^2=-c/a+b^2/4a^2

since b^2/4a^2 = (b/2a)^2

we get

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

LHS is in a2+2ab+b2

======>x^2+(b/a)x+(b/2a)^2=(x+b/2a)^2

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

apply square root on both sides we get

x+b/2a=√(-c/a+(b/2a)^2)

x=-b/2a+√(-c/a+(b/2a)^2)

multiply both sides by 2a/2a

and further simplifying the (-c/a+(b/2a)^2

we get

x = (-b ± √ (b² - 4ac) )/2a.