Question

write a quadratic equation with the given roots. write the equation in the form ax^2+bx + c = 0 where a, b, and c are integers.
3/2, 1/4


A. 8x^2 - 14x + 3 = 0
B. 8x^2 - 3x + 14 = 0
C. 4x^2 - x + 6 = 0
D. 4x^2 - 6x + 1 = 0

Answer 1

if a quadratic equation has roots \(r_1\) and \(r_2\), then it can be written as:\[a(x-r_1)(x-r_2)=0\]if you expand this you will get:\[a(x^2-(r_1+r_2)x+r_1r_2)=0\]this should help you work out the answer

Answer 2

i dont know what that is..

Answer 3

'a' in the equation above is some arbitrary constant - so you can ignore that for this problem - assume its equal to 1.
so you are left with:\[x^2-(r_1+r_2)x+r_1r_2=0\]

Answer 4

just substitute the values given to you for \(r_1\) and \(r_2\).

Answer 5

in your case:\[r_1=\frac{3}{2}\]\[r_2=\frac{1}{4}\]

Answer 6

so what is the value of \(r_1+r_2\)?

Answer 7

7/4

Answer 8

good, now what is the value of:\[r_1\times r_2\]

Answer 9

3/8

Answer 10

great!, so just substitute these into this equation:\[x^2-(r_1+r_2)x+r_1r_2=0\]what do you end up with?

Answer 11

x^2 - (7/4)x + 3/8 = 0

Answer 12

perfect! now we need to get rid of those nasty fraction. so just multiply everything by 8. what do you end up with?

Answer 13

14.

Answer 14

3

Answer 15

yes - so what does the final equation look like?

Answer 16

remember you needed to multiply EVERYTHING by 8, so:

8(x^2 - (7/4)x + 3/8) = 8*0

Answer 17

which expands to:

8x^2 - 8(7/4)x + 8(3/8) = 0

Answer 18

8x^2 - (14)x+(3) = 0

Answer 19

thats it! great work! :)

Answer 20

whats r?

Answer 21

where do you see r?

Answer 22

do you mean \(r_1\) and \(r_2\)?

Answer 23

its the answer.
r = 36,
r = 12
r = 51
r = 13

Answer 24

what is the full question?

Answer 25

oh nvm.

Answer 26

ok :)

Answer 27

thansk

Answer 28

yw :)