Answer:
The zeroes are [tex]x=4[/tex] and [tex]x=-5[/tex]
On the graph, each of these zeroes represent the x-value where the equation will intersect with the x-axis.
Step-by-step explanation:
We have the quadratic equation [tex]y=x^2+x-20[/tex]
To factor this we need to find two numbers that fulfill the following:
They add up to 1
They multiply to give you -20
These two numbers are -4 and 5
This means that the quadratic equation in its factored form will be: [tex]y=(x-4)(x+5)[/tex]
Now that we have the factored form, we need to set [tex]y=0[/tex] and solve for x
From this factored form, we can see that when [tex]x=4[/tex] and [tex]x=-5[/tex] the result will be zero. Just to check we can plug in each of these x values
[tex](x-4)(x+5)=0\\\\(4-4)(4+5)=0\\\\0*9=0\\\\0=0[/tex]
[tex](x-4)(x+5)=0\\\\(-5-4)(-5+5)=0\\\\(-9)*(0)=0\\\\0=0[/tex]
The result of this confirms that x=4 and x=-5 are indeed the zeroes of this equation.
Each of these zeroes represent the x-value where the equation will intersect with the x-axis.
