Question

Find the sum and the product of the roots of the equation: x^2+35x−51=0

what is the product of them?

Answer 1

(a)

`Sum = -35`

`Product = -51`

(b)

`Product = 1785`

Explanation:

Given

`x^2 + 35x - 51 = 0`

Required

(a) Determine the sum and product of the equation

(b) Determine the products of the (a)

Solving (a)

The general form of a quadratic equation is:

`ax^2 + bx + c = 0`

Where

`Sum = -(b)/(a)`

`Product = (c)/(a)`

By comparison of
`ax^2 + bx + c = 0` tp
`x^2 + 35x - 51 = 0`

`a = 1`

`b = 35`

`c = -51`

So:

`Sum = -(b)/(a)`

`Sum = -(35)/(1)`

`Sum = -35`

`Product = (c)/(a)`

`Product = (-51)/(1)`

`Product = -51`

Solving (b)

From (a) above, we have:

`Sum = -35`

`Product = -51`

Their product is:

`Product = -35 * -51`

`Product = 1785`