Question

Factorising Quadratics


`12x^(2) +x-15=(6x+?)(2x-?)`


Find the missing numbers.


I'm not entirely sure if this is possible, as my teacher is prone to making typos but I have no idea how to solve this; I've tried trial and error with factors of 15 and none of them seem to work!

Answer 1

quadratic formula where:

`ax ^(2) + bx + c`

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

`\frac{ - b - \sqrt{b { }^(2) - 4ac } }{2a}`
do both do get the roots of the equation

Answer 2

Explanation:

A short answer is that you cannot factor this the way you are trying to do it. What to do to go on is a question. You could use the quadratic formula to get some sort of answer but if factoring is your only option, forget about it.

Here's how you can check.

• a = 12
• b = 1
• c = -15

There is a part of the quadratic solution is the sqrt(b^2 - 4*a*c). In order to be factorable, this sqrt must result in a perfect square.

sqrt(1 - 4(12)(-15) ) = sqrt( 1 - - 720) = sqrt(721)

This is anything but a perfect square. (721 does factor, however, into 7 * 103). I03 is prime. So the long and short of it is, there's no way it will factor.