Question

1. Without solving the equation, find the sum and product of its solutions.(a) x^2 + 7x - 11 = 0 b) 3x^2 - 5x - 9 = 0.

Answer 1

Given

The equation is given as

`\begin{gathered} a.x^2+7x-11=0 \\ b.3x^2-5x-9=0 \end{gathered}`Step-by-step explanation

a. The equation is given as

`x^2+7x-11=0`

The general equation is

`ax^2+bx+c`

The sum of the root is determined as

`(-b)/(a)`

Substitute the values from the given equation.

`-(b)/(a)=-(7)/(1)`

The product of roots is determined as

`(c)/(a)`

Substitute the values from the given equation.

`(c)/(a)=-(11)/(1)=-11`

b. The equation is given

`3x^2-5x-9=0`

The sum of root is

`(-b)/(a)=-(-5)/(3)=(5)/(3)`

The product of root is

`(c)/(a)=-(9)/(3)=-3`Answer

a. The sum of root is -7.

The product of root is -11.

b. The sum of root is 5/3.

The product of root is -3.