Question 59580: Could I please get some assistance with this?
Find the roots of the expression - factor the quadratic expression completely:
6x^2 - 42x + 72
Thank you!
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! 6x^2 - 42x + 72
To factorise this, we need to find 2 numbers whose sum is -42 and whose product = 6*72 = 432
We find the numbers to be - 18 and - 24
Now 6x^2 - 42x + 72
= 6x^2 - 18x - 24x + 72 [splitting the middle term]
= 6x(x - 3) - 24(x - 3) [Removing the common factor]
= (x - 3) (6x - 24)
= (x - 3) (6) (x - 4) [Removing the common factor]
So 6x^2 - 42x + 72 = 6(x - 3)(x - 4)
To find the roots, we equate this to zero.
==> 6(x - 3)(x - 4) = 0
==> x - 3 = 0 or x - 4 = 0
==> x = 3 or x = 4
So 3 and 4 are the roots of the given equation.
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