Question

3x^2+bx+24=0 if one of its root is 3

Answer 1

Other root of equation,
`(8)/(3)`

Value of (
`b`),
`-17`

Explanation:

The given quadratic equation is in standard form. Standard form is the basic format of representing a quadratic equation, a quadratic equation in standard form would use the following format,

`y=ax^2+bx+c`

To solve this problem, one could use Vieta's theorems. Vieta's theorems state the following, let (
`x_1`) and (
`x_2`) represent the roots of the equation,

`(x_1)+(x_2)=-(b)/(a)`

`(x_1)(x_2)=(c)/(a)`

Substitute the given values into the equation,

`3+(x_2)=-(b)/(3)`

`(3)(x_2)=(24)/(3)`

Simplify,

`(3)+(x_2)=-(b)/(3)`

`(3)(x_2)=8`

Inverse operations,

`(3)+(x_2)=-(b)/(3)`

`x_2=(8)/(3)`

Substitute in the value of (
`x_2`),

`(3)+((8)/(3))=-(b)/(3)`

Simplify, convert to improper fractions and combine like terms,

`(9)/(3)+(8)/(3)=-(b)/(3)`

`(17)/(3)=-(b)/(3)`

Multiply both sides of the equation by (
`3`) to remove the denominator,

`17=-b`