Question

Let ​ f(x)=x^2−13x+30 . What are the zeros of the function? ____ and ____

Answer 1

Answer:

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

Step-by-step 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.

Answer 2

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 !!