Question

How do you find all the zeros of `y=x^2-11x+30` with its multiplicities?

Answer 1

`x = 5, 6`

Explanation:

Write out a set of brackets like this

`(x + a)(x + b)`

You should find two constants, `a` and `b`, such that

`a + b = -11`
`a * b = 30`

Which you can do by trial and error, so

`a = -5`
`b = -6`

Therefore the fully factorised form of the equation is

`(x - 5)(x - 6) = 0`

Solving for the roots or zeros of this:

For the entire quadratic to equal zero, one or both of the pairs of brackets must equal `0`, so solve for each individual one and you will end up with two answers.

`x - 5 = 0 -> x = 5`
`x - 6 = 0 -> x = 6`

Therefore,

`x = 5, 6`