# The positive difference between the zeroes of the quadratic expression #x^2 + kx +3# is #sqrt(69)#. What are the possible values of k?

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The book section is about the determinant, answer given by the book is : +/- 9.

I get that the determinant is: #k^2 -12#

and that 69 + 12 = 81, ans #sqrt(81) = 9)# . However, I am confuse by that direct math manipulation to put 12 in the square root. and the formulation use of "The difference between zeroes"

The book section is about the determinant, answer given by the book is : +/- 9.

I get that the determinant is:

and that 69 + 12 = 81, ans

##### 1 Answer

The quadratic formula is:

The first root is:

The second root is:

We want:

Substitute equations [1] and [2] into equation [3]:

Combine the two fractions over the common denominator:

Simplify:

Substitute

Multiply

we can square both sides:

Add 12 to both sides:

Take the square root of both sides (don't forget the