M4maths Previous Puzzles

09 Apr 2014 Quadratic equation

Solve
2x^4+9x^3+8x^2+9x+2 = 0

OPtion

1) x = -2 (+-) sqrt 5
2) x = -2 (+-) sqrt 3
3) x = -4 (+-) sqrt 5
4) x = -3 (+-) sqrt 3
5) x = -5 (+-) sqrt 3
6) x = -2 (+-) sqrt 7
7) x = -2 (+-) sqrt 2
8) x = -3 (+-) sqrt 3
9) x = -4 (+-) sqrt 3
10)None of these

Solution

In this equation
divide the equation by x^2 to get,
2[x^2+(1/x^2)]+9[x+(1/x)]+8 = 0
Let [x+(1/x)] = t
solve
x = -2 (+-) sqrt 3

Option 2)

Correct Option: 2 Best Solution (8)

Ann Theressa   10 years AGO

Divide the equation by x^2

2x^2 + 9x + 8 + 9/x +2/x^2 = 0
2(x^2+1/x^2) + 9(x+1/x) +8 = 0

put (x+1/x) = y
so, (x^2 + 1/x^2) = y^2 - 2

2(y^2 - 2) +9y + 8 = 0
2y^2 + 9y + 4 = 0

Solving y = -4 , -1/2

when y = -4
x + 1/x = -4
x^2 + 4x + 1 = 0

x = -4(+-)sqrt(16-4)/2

x = -2(+-)sqrt 3

Like? Yes (13) | No (6)  

Kaleem Pasha   10 years AGO

Answer 2

Like? Yes (3) | No (2)  

AVIJIT   10 years AGO

if we calculte thish equation we will get 2 real roots and 2 complex roots and these are
x1 = -0.25+0.9682458i
x2 = -0.25-0.9682458i
x3 = -0.2679492
x4 = -3.7320508
so if we go for 2nd option then -2(+-)sqrt(3)
we got -3.7320 nad -0.267 that same with x3 nad x4

Like? Yes (2) | No (1)  

Md Shahid Akhter   10 years AGO

on factorising we get (2x^2+x+2)(x^2+4x+1)=0
for second factor i.e
x^2+4x+1=0
x=-2(+-)sqrt(3)
So,
Ans is 2nd option

Like? Yes (3) | No (2)  

ABY   10 years AGO

if we calculte thish equation we will get 2 real roots and 2 complex roots and these are
x1 = -0.25+0.9682458i
x2 = -0.25-0.9682458i
x3 = -0.2679492
x4 = -3.7320508
so if we go for 2nd option then -2(+-)sqrt(3)
we got -3.7320 nad -0.267 that same with x3 nad x4

Like? Yes (1) | No (1)  

ABYSUP   10 years AGO

if we calculte thish equation we will get 2 real roots and 2 complex roots and these are
x1 = -0.25+0.9682458i
x2 = -0.25-0.9682458i
x3 = -0.2679492
x4 = -3.7320508
so if we go for 2nd option then -2(+-)sqrt(3)
we got -3.7320 nad -0.267 that same with x3 nad x4

Like? Yes (1) | No (2)  

avi   10 years AGO

if we calculte thish equation we will get 2 real roots and 2 complex roots and these are
x1 = -0.25+0.9682458i
x2 = -0.25-0.9682458i
x3 = -0.2679492
x4 = -3.7320508
so if we go for 2nd option then -2(+-)sqrt(3)
we got -3.7320 nad -0.267 that same with x3 nad x4

Like? Yes (1) | No (2)  

MD SOHAIL AKHTER   10 years AGO

by substituting the values given in option we get
x=-2(+-)sqrt 3
so option (2) is correct

Like? Yes (2) | No (4)