Question

Given the quadratic function 3x^(2) =8x-5 what are the values of x?

Answer 1

3x^2 = 8x - 5

3x^2 - 8x + 5 = 0 move all terms to one side

3x^2 - 3x - 5x + 5 = 0 split them into two terms

3x(x - 1) - 5(x - 1) = 0 factor out common terms in the first two terms, then the last two terms.

(x - 1)(3x - 5) = 0

x = 1, 5/3

hope this helped, God bless!

Answer 2

The values of x are
`(5)/(3)` and 1.

Explanation:

Given quadratic function
`3x^2=8x-5`

We have to solve for x.

Consider the given quadratic function
`3x^2=8x-5`

This can be written as
`3x^2-8x+5=0`

We can solve the above quadratic equation using middle term split method,

-8x can be written as -3x - 5x

Thus, the equation becomes,

`3x^2-8x+5=0`

`\Rightarrow 3x^2-3x-5x+5=0`

Taking 3x common from first two term and -5 common from last two terms, we get,

`\Rightarrow 3x(x-1)-5(x-1)=0`

`\Rightarrow (3x-5)(x-1)=0`

Now using zero product property
`a.b=0 \Rightarrow a=0\ or\ b=0` , we have,

`\Rightarrow (3x-5)=0` or
`\Rightarrow (x-1)=0`

`\Rightarrow x=(5)/(3)` or
`\Rightarrow x=1`

Thus, The values of x are
`(5)/(3)` and 1.