Question

How do you use the quadratic formula to find the zeros of the function `12x^2 - 5x - 7 = 0`?

Answer 1

Zeros of the function are `x= 1 and x= -7/12`

Explanation:

`12 x^2 -5x -7 =0 or 12 x^2 -12x + 7x -7 = 0` or

`12 x(x-1) + 7(x -1) = 0 or (x-1)(12x+7) =0`

Zeros are either `x-1 =0 :. x =1` OR `12x+7 =0 :. x = -7/12`

Zeros of the function are `x= 1 and x= -7/12` [Ans]

Answer 2

zeroes: `x in {-7/12, 1}`

Explanation:

The quadratic formula tells us us that if an equation has the form:
`color(white)("XXX")color(red)ax^2+color(blue)bx+color(green)c=0`
then it has zeroes:
`color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(green)c))/(2color(red)a)`

Therefore
`color(white)("XXX")color(red)(12)x^2color(blue)(-5)xcolor(green)(-7)=0`
has zeroes:
`color(white)("XXX")x=(-color(blue)((-5))+-sqrt(color(blue)((-5))^2-4 * color(red)(12) * color(green)((-7))))/(2*color(red)(12))`

`color(white)("XXXX")=(5+-sqrt(25+336))/24`

`color(white)("XXXX")=(5+-19)/24`

`color(white)("XXXX")= 1 " or " -7/12`

Answer 3

Zeros are `x= 1 or x =-7/12`

Explanation:

`x = - -b/(2a) +- sqrt(b^2-4ac)/(2a ); a=12 , b= -5 ,c =-7 ;`

`D=b^2-4ac= 25+336= 361 :. x = 5/24 +- 19/ 24`

`x = 5/24 +19/24 or x= 1 or x = 5/24 - 19/24 = -14/24 = -7/12`

Zeros are `x= 1 or x =-7/12` [Ans]