0
15x2 - 17x + 4 = 15x2 - 5x - 12x + 4
= 5x(3x - 1) - 4(3x - 1).
= (5x - 4)(3x - 1).
Thus the solution,
when 15x2 - 17x + 4 = (5x - 4)(3x - 1) = 0,
is: x = 4/5 or 1/3.
* * * * *
The technique, in case it is not familiar, is quite simple:
Step 1: Note that the three co-efficients of the given quadratic are 15, -17, and 4.
Step 2: We seek two numbers whose sum and product are -17 and 60.
(Note that 60 is, itself the product of 15 and 4.)
The two numbers we seek are -5 and -12.
Step 3: Replace the middle term, '-17x' with two terms, '-5x' and '-12x'.
Step 4: Continue factorisation easily, as shown. Then, combine like terms.
Step 5: To find solution, apply the following principle: The product of two factors is equal to zero if, and only if, one or other of the two factors is equal to zero.
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