Question

Let ​ f(x)=x^2−13x+30 .

What are the zeros of the function?

____ and ____

Answer 1

x^2-13x+30
x^2-10x-3x+30
x(x-10)-3(x-10)
(x-3)(x-10)

so two zeors are 3 and 10 !!

Answer 2

The zeros of the given function
`f(x)=x^2-13x+30` are 3 and 10

Explanation:

Given : Function
`f(x)=x^2-13x+30`

We have to find the zeros of the given function
`f(x)=x^2-13x+30`

Consider the given function
`f(x)=x^2-13x+30`

Since, we have to find the zeros of the given quadratic equation
`f(x)=x^2-13x+30`

Put f(x) = 0

That is
`x^2-13x+30=0`

Now we will solve the above quadratic equation using middle term splitting method,

-13x can be written as -3x- 10x

`x^2-10x-3x+30=0`

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

`=x\left(x-3\right)-10\left(x-3\right)`

Taking (x- 10) common, we have,

`\left(x-3\right)\left(x-10\right)=0`

Using zero product rule,
`a\cdot b= 0 \Rightarrow a=0 \ or\ b=0`

`\left(x-3\right)=0` and
`\left(x-10\right)=0`

Simplify, we have,

`x=3` and
`x=10`

Thus, The zeros of the given function
`f(x)=x^2-13x+30` are 3 and 10.