Question

How do you solve `7z ^ { 2} - 8z - 1= 0`?

Answer 1

Solution: `z~~ 1.26(2dp) , z~~ -0.11(2dp)`

Explanation:

Comparing with standard quadratic equation `ax^2+bx+c =0` we get `7z^2-8z-1 =0 ; a=7 ; b= -8 ; c= -1 D=b^2-4ac = 92` Discriminant (D) is positive , so roots are real.

Roots are `z= -b/(2a) +- sqrt (b^2-4ac)/(2a) or z = 8/14 +- sqrt 92/14 :. z~~ 1.26(2dp) , z~~ -0.11(2dp)`

Solution:`z~~ 1.26(2dp) , z~~ -0.11(2dp)`[Ans]

Answer 2

`color(red)(z=(4+sqrt23)/7` or `color(red)(z=(4-sqrt23)/7`

Explanation:

`7z^2-8z-1=0`

`:.x=(-b+-sqrt(b^2-4ac))/(2a)`

`:.x=(-(-8)+-sqrt((-8)^2-4(7)(-1)))/(2 xx 7)`

`:.(8+-sqrt(64+28))/14`

`:.(8+-sqrt92)/14`

`:.(8+-sqrt(23*2*2))/14`

`:.color(red)(sqrt2*sqrt2=2`

`:.(8+-2sqrt(23))/14`

`(cancel2^color(red)1(4+-sqrt(23)))/cancel14^color(red)7`

`:.color(red)((4+sqrt(23))/color(red)7` or `color(red)((4-sqrt(23))/7`