Assuming that the roots of the given qudratic equation are a, b find the sum and product of the roots.

Sum of root a+b = -c/d

Product of root ab= e/d

Step-by-step 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

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