resolve the following into factories: 3x²+5x-2
Answers
Answer:
Quadratic formula:
x = (-b +/-(square root)b^2–4ac)/2a
a = 3
b = 5
c = 2
x = (-5 +/- (square root)25–4*3*2)/2*3
x = (-5 +/- (square root)25–24)/6
x = (-5 +/-(square root)1)/6
x = (-5 +/- 1)/6
x = -6/6 OR x = -4/6
Reduce the fractions:
x = -1 OR x = -2/3
Now substitute for each value of x in the original equation:
3x^2 + 5x + 2 = 0
x = -1
3*-1^2 + 5*-1 + 2 = 0
3*1 - 5 + 2 = 0
3–5+2 = 0
-2 + 2 = 0
0 = 0
Okay! So x = -1 is a valid solution to this equation. Now for the other value:
3x^2 + 5x + 2 = 0
x = -2/3
3*(-2/3)^2 + 5 * (-2/3) + 2 = 0
3 * (4/9) - 10/3 + 2 = 0
12/9 - 10/3 + 2 = 0
Multiply all terms by 9 to eliminate both denominators:
(9)12/9 - 9(10/3) + 2*9 = 0
12–30+18 = 0
-18 + 18 = 0
0 = 0
Explanation:
at the place of - it is +.
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