Question

What is an example of an equation with 2 real zeros?

Answer 1

x(x - 1) = 0

Answer 2

becca, can you make such equation on your own now?
ask doubts, you'll learn more...

Answer 3

I have tried to come up with an equation. I'm homeschooled and my lessons do not add much detail to help me learn.

Answer 4

oh, you tried, good
what did u have ?

Answer 5

I have tried the equation -4x^2+3x because the equation also has to be an upward opening parabola

Answer 6

in \(ax^2+bx+c=0\)
if a is positive, then parabola opens upward
if a is negative then parabola opens downwards.

NOTE : -4x^2+3x is an EXPRESSION
and EQUATION has "=" sign, like -4x^2+3x =0 or -4x^2+3x =-10

Answer 7

so, try again to get equation with upward opening parabola ?

Answer 8

The leading coefficient then has to become positive, so 4x^2+3x works

Answer 9

but thats an expression
where is the equation ?

Answer 10

That's where I am confused. It's a story problem that is in three parts and none of it makes any sense

Answer 11

I'm not sure what real zeros are because they didn't mention them until now.

Answer 12

you know what real numbers are ?

Answer 13

and i was just asking for equation, 4x^2+3x =0
will work as an equation with parabola openeing upwards and real zeros

Answer 14

How do I know there are 2 real zeros?

Answer 15

a polynomial with degree 'n' has 'n' zeros.
does this make sense ? know what is a degree of polynomial ?

Answer 16

degree is the highest exponent of 'x'
you knew this ?

Answer 17

The degree would be a 3rd degree trinominal, correct?

Answer 18

Oops no. 3rd degree binomial

Answer 19

how do you find degree ?

Answer 20

what is the highest exponent of 'x' in \(ax^2+bx+c=0\)
?

Answer 21

I learned that you add the exponets together for the degree... I'm assuming that is wrong.

Answer 22

Would it be 2?

Answer 23

yes!
and if there are more than 1 variables, then you ADD exponents, but here there's only 1 variable , 'x'
so, degree = 2, so it MUST HAVE 2 'zeros'
like in \(ax^7+bx^2+x+1=0\), the highest exponent = degree = 7
so this will have 7 'zeros'
understanding this ?

Answer 24

This is making a lot more sense!!!

Answer 25

When it says an upward parabola does it mean the vertex is pointing up or down?

Answer 26

nice!!
so, when you were asked to have '2' zeros, you will make an equation with highest exponent = 2
so, use ax^2+bx+c = 0 , put values of a,b,c

but ax^4+bx^2+d =0 will not work because degree =4 and it will have more than 2 zeros