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

Answer: 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