Question

Question #78f69

Answer 1

`x=-3/2" or "x=2/3`

Explanation:

`6x^2+5x-6=0" is in standard form"`

`"that is "ax^2+bx+c color(white)(x);a!=0`

`"to factorise consider the factors of ac which sum to b"`

`"the factors of - 36 which sum to + 5 are + 9 and - 4"`

`6x^2+9x-4x-6=0larrcolor(blue)"split the middle term"`

`"factorise by 'grouping'"`

`color(red)(3x)(2x+3)color(red)(-2)(2x+3)=0`

`rArr(2x+3)(color(red)(3x-2))=0`

`"equate each factor to zero and solve for x"`

`2x+3=0rArrx=-3/2`

`3x-2=0rArrx=2/3`

Answer 2

`(2/3, 0) and (3/2, 0)`

Explanation:

`6x^2+5x-6=0`
`(3x-2)(2x+3)=0`

Therefore, each factor set equal to `0` gives:
`x = 2/3 or -3/2`

Therefore, the roots are `x=2/3 and x=-1.5.`

In the quadratic equation curve of `y=6x^2+5x-6` the two roots result with `y =0`.

Hence, their coordinates are `(2/3,0) and (-1.5,0).`