Question

what are the values of x that are solutions to f(x)=0 where f(x)=-5x^2+4x+9

Answer 1

\[\large{-5x^2 + 4x + 9 =0}\]

\[\large{\implies 5x^2 - 4x - 9 = 0}\]

Answer 2

Any doubt till this step ?

Answer 3

I just multiplied (-1) on both sides

Answer 4

\[\large{5x^2 +5x - 9x - 9 = 0}\]

Answer 5

the choices are

a -0.56,0.44
b-5,4
c-0.80,-1.80
d-1.00,-1.80

Answer 6

We will get to that later :)

First tell me do you have any doubt in the steps I wrote above ?

Answer 7

yes because none of those are any of the available answers

Answer 8

No no no ... I have not calculated the answer yet.. We are just doing some work to get the answer :)

Answer 9

ok got ya

Answer 10

Good lets see:

\[\large{5x^2 + 5x - 9x - 9 = 0}\]

\[\large{\implies 5x(x +1) - 9(x+1) = 0}\]

Answer 11

you asking me to distribute this?

Answer 12

\[\large{\implies (5x-9)(x+1) = 0}\]

\[\large{\implies (5x-9) = 0 ~\rm{or}~(x+1) = 0}\]

Answer 13

Nope not distribution, collecting the terms

Answer 14

different problem

Answer 15

Remember this:

\[\large{xy = 0 \implies x = 0 ~or~y = 0}\]

Answer 16

Thus:

\[\large{(5x-9)(x+1) = 0}\]

\[\large{\implies 5x - 9 = 0 ~or~x+1 = 0}\]

Answer 17

Now solve each expression one by one:

1. 5x - 9 = 0

=> 5x = 9

=> x = 9/5

2. x+1 = 0

=> x = -1

Answer 18

Any doubt ?