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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Alik [6]

Answer:

$d=28.28$

Step-by-step explanation:

To calculate the lenght of the diagonal d across the square, we can assume that the square it is compound of two right triangles. So, we can resolve this exercise using The Pythagorean Theorem.

The Pythagorean theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.

If in a right triangle there are legs of length a and b, and the measure of the hypotenuse is c, then the following relation is fulfilled:

$a^{2} +b^{2} =c^{2}$ a is the height, b is the base, and c is