Determine whether x=2/3 and x=3/4 are solutions of the equation 12x2 -17x+6=0
Answers
Question :- Determine whether x=2/3 and x=3/4 are solutions of the equation 12x² - 17x + 6 = 0 ?
Solution :-
we know that, if x is a solution of any equation . then,
- f(x) = 0 .
checking at x = (3/4) now :-
→ f(x) = 12x² - 17x + 6
→ f(3/4) = 12(3/4)² - 17(3/4) + 6
→ f(3/4) = 12(9/16) - (51/4) + 6
→ f(3/4) = (27/4) - (51/4) + 6
→ f(3/4) = (27 - 51 + 24)/4
→ f(3/4) = (51 - 51)/4
→ f(3/4) = 0/4
→ f(3/4) = 0 .
Therefore, x = 3/4 is a solution of given equation .
checking at x = (2/3) now :-
→ f(x) = 12x² - 17x + 6
→ f(3/4) = 12(2/3)² - 17(2/3) + 6
→ f(3/4) = 12(4/9) - (34/3) + 6
→ f(3/4) = (16/3) - (34/3) + 6
→ f(3/4) = (16 - 34 + 18)/3
→ f(3/4) = (34 - 34)/3
→ f(3/4) = 0/3
→ f(3/4) = 0 .
Therefore, x = 2/3 is a solution of given equation.
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