Question

What are the zeros of the quadratic function f(x) = 6x2 + 12x - 7?
​

Answer 1

`(-6+√(78) )/(6)` and
`(-6-√(78) )/(6)`

Explanation:

We are asked that what are the zeros of the quadratic function f(x) = 6x² +12x -7.

So, we have to find the roots of the equation, f(x) = 6x² +12x -7 =0 ...... (1)

Since the quadratic function can not be factorized, so we have to apply Sridhar Acharya's formula.

This formula gives if, ax² +bx +c =0, the the two roots of the equation are

`\frac{-b+\sqrt{b^(2)-4ac } }{2a} , \frac{-b-\sqrt{b^(2)-4ac } }{2a}`

Therefore, in our case 'a' being 6, 'b' being 12 and 'c' being -7, the two roots of the equation (1) will be

`\frac{-12+\sqrt{12^(2)-4*6*(-7) } }{2*6},  \frac{-12-\sqrt{12^(2)-4*6*(-7) } }{2*6}`

=
`(-12+√(312) )/(12),(-12-√(312) )/(12)`

=
`(-6+√(78) )/(6)` and
`(-6-√(78) )/(6)`

Hence, x=
`(-6+√(78) )/(6)`

and x=
`(-6-√(78) )/(6)`

(Answer)