How do you solve for x in this quadratic equation?: 5x^2 – 34x + 24 = 0

1 answer:

5 0

Quadratic formula
factoring
graphing
completing the square
factoring by grouping
Rational Roots Theorem
synthetic division

Take a look at 5x^2 – 34x + 24 = 0. The last term could have been the result of these different possible muliplications: 1*24, 2*12, 3*8, 4*6. The leading term is 5, whose factors are 5 and 1. Thus, possible rational roots would be
4/5 (the 4 is a factor of 24 and the 5 is a factor of 5) and 6/1 (the 6 is a factor of 24 and the 1 is a factor of 5).

Using synth. div. to check whether 6 is actually a root:
___________________
6 / 5 -34 24
30 -24
------ --------------------------
5 -4 0

since the remainder is 0, we can safely call 6 a "root."
Note the remaining coefficients, 5 and -4:

They correspond to the factor 5x - 4. If we set this difference = to 0, and solve for x, we get x = 4/5 (which is correct).

The roots of 5x^2 – 34x + 24 = 0 are x = 4/5 and x= 6/1.

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