Question

chapter 2:Quadratic Equations

Answer 1

If a and B are the roots of the quadratic equation \[\frac{ 2x-3 }{ 8 }=\frac{ 3-2x }{ 5x },\]find the value of \[a^2+b^2\]

Answer 2

the standard form for a quadratic equation is

ax^2 + bx + c = 0

product of roots AB = c/a
and A + B = -b/a

first rearrange your equation to the standard form

Answer 3

i got \[10x^2+x-24=0\]

Answer 4

then to find A^2 + B^2 use
the identity A^2 + B^2 = (A + B)^2 - 2AB

Answer 5

\[a+B=-\frac{ 1 }{ 10 }=SOR\]\[aB=-\frac{ 12 }{ 5 }=POR\]

Answer 6

yes

Answer 7

I don't understand how u get -2aB

Answer 8

(a +B)^2 = a^2 +2aB + B^2

Answer 9

now take away the 2aB

Answer 10

Okay

Answer 11

now you just plug in the values for a +B and aB

Answer 12

\[(a+B)^2-2aB=(-\frac{ 1 }{ 10 })^2-2(-\frac{ 12 }{ 5 })\]

Answer 13

\[=\frac{ 1 }{ 100 }+\frac{ 24 }{ 5 }\]

Answer 14

\[=\frac{ 481 }{ 100 }\]

Answer 15

Thnx @welshfella

Answer 16

looks good yw