Answer: Sum of root a+b = -c/d
Product of root ab= e/d
Explanation:
Let the general quadratic equation be dx² + cx + e = 0
And the root of the equation be
'a' and 'b'
Using the general formula to find the solution to the quadratic equation
a = -c+√c²- 4de/2d
b = -c-√c²- 4de/2d
Taking the sum of the roots
a+b = (-c+√c²- 4de/2d) + (-c-√c²- 4de/2d)
a+b = (-c-c+√c²- 4de/2d - √c²- 4de/2d)/2d
a+b = -2c/2d
a+b = -c/d
The sum of the root of the quadratic equation will be -c/d
Product of roots
ab = (-c+√c²- 4de/2d)(-c-√c²- 4de/2d)
= {c² +(c√c²- 4de)- (c√c²- 4de) -(c²-4de)}/4d²
= {c²-c²+4de}/4d²
= 4de/4d²
= e/d
The product of the above quadratic equation will be e/d