find value of x?

Question

4x^3 + 14x^2 -6x-12=0 find value of x

(a)( 9-sqrt(32))/2

(b)(9-sqrt(47))/2

(c)(9+sqrt(33))/4

(d)3/2

(e)None of these

I need to choose an answer from the above with less time consuming

what should i choose ?

please explain your answer .

Answer 1

OK,
first of all you can divide the whole equation by 2:

2x³ + 7x² - 3x - 6 = 0

x = 1 obviously satisfies the equation:

2·1³ + 7·1² - 3·1 - 6 = 2 + 7 - 3 - 6 = 0

Now, using the synthetic division / Horner's algorythm , long division or otherwise factor:

(x - 1)(2x² + 9x + 6) = 0

Apart from x = 1, there are two more solutions for x, satisfying
2x² + 9x + 6 = 0

Use quadratic formula:
x = [-9 ± √(9² - 4·2·6)] / 2·2
x = [-9 ± √33] / 4

So all three solutions are
x = 1, x = [-9 + √33] / 4 and x = [-9 - √33] / 4

Since none of them are among the numerical answers given, the answer is

(e)None of these
_____

Hope this helps.

Answer 2

As the ans are in sqrt so it difficult to put the values directly. Being a cubic equation its first factor is found by hit n trial which are usually 1 or -1. In this equation , the factor is x=1
1| 4 14 -6 -12
| 0 4 18 12
_________________
4 18 12 0
the above display is an easy way to divide a cubic equation if one factor is known. In this the coefficient of x^3,x^2,x ,& the constants are written .then the factor is written at the side of the margin.0 is written under the coef. of x^3 then we get the remainderby subtracting it from the coeff. then we write the remainder under the coef. of x^2 & again subtract.till you get the last remainder as 0.It is imp. that you get the last remainder as 0 If you don't get then its a proof that your selection of the factor is wrong. Now you multiply the integers with x^2 ,x, 1 respectively so that you get a quadratic equation.In the above case , you get 4x^2 + 18x + 12= 0.You solve it by applying the fomula:
x= ( -b +/- sqrt b^2 - 4ac )/2a
You get x = (-9 +/- sqrt 33)/4.So the ans is e) None of these.
You might find the above method of solving cubic equation a little tricky , but when you will practice it in 2-3 questions you will definitely find it a better & an easy way of solving it.I hope this method helps you in solving the questions faster

Answer 3

if we factor this we have
4x^3+14x^2-6x-12=2(x-1)(2x^2+9x+6)=0
x=1
2x^2+9x+6=0 ==>
x= (-9 -sqrt(33))/4
x=(-9 +sqrt(33))/4

Answer 4

The 'easy' way is to try each one and see if the answer is 0.
(with an excel spreadsheet, this should be easy -- I did it in less than 2 minutes).

The other way is to find a root (I found r = +1) and divide by x-r -- in this case, (x-1). This leaves a simpler (quadratic) equation.

Answer 5

4x^3+14x^2-6x-12=0
4x^2(x-1)+18x(x-1)+12(x-1)=0
(x-1(4x^2+18x+12)=0
x=1OR
4x^2+18x+12=0
2x^2+9x+6=0
x=1/4[-9+/-sqrt(81-48)]
=1/4[-9+/- sqrt(33)].
x=1,1/4[-9+/-sqrt(33)].answer- none of the options