How do you use the quadratic formula to find the zeros of the function 12x^2 - 5x - 7 = 012x2−5x−7=0?

3 Answers
Binayaka C.
Jul 29, 2017

Zeros of the function are x= 1 and x= -7/12x=1andx=−712

Explanation:

12 x^2 -5x -7 =0 or 12 x^2 -12x + 7x -7 = 012x2−5x−7=0or12x2−12x+7x−7=0 or

12 x(x-1) + 7(x -1) = 0 or (x-1)(12x+7) =0 12x(x−1)+7(x−1)=0or(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]

Alan P.
Jul 29, 2017

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

Binayaka C.
Jul 29, 2017

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]

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