What are the approximate values of the non-integral roots of the polynomial equation? –5.57 –1.95 0.21 1.27 4.73

Question

asked Nov 4, 2020 214k views

2 Answers

Shankar Guru · Answer 1 · 2020-11-10T13:17:32+0000

Answer:

Option 4 and 5.

Explanation:

Consider the given polynomial equation is

x^(4)-4x^(3)=6x^(2)-12x

We need to find approximate values of the non-integral roots of the polynomial equation.

x^(4)-4x^(3)-6x^(2)+12x

Find factor form.

x(x^(3)-4x^(2)-6x^(1)+12)

For x=-2 the value of parenthesis is 0. It means (x+2) is a factor of parenthesis.

Divide the parenthesis by (x+2). After division remainder is 0 and quotient is
(x^2 - 6 x + 6) , so the factor form is

x (x + 2) (x^2 - 6 x + 6)

Equate the factor form equal to 0, to find the roots.

x (x + 2) (x^2 - 6 x + 6)=0

x=0

$x+2=0\Rightarrow x=-2$

x^2 - 6 x + 6=0 .... (1)

Quadratic formula for
ax^2+bx+c=0 is

$x=(-b\pm √(b^2-4ac))/(2a)$

In (1), a=1, b=-6, c=6. Using quadratic formula we get

$x=(-(-6)\pm √((-6)^2-4(1)(6)))/(2(1))$

$x=(6\pm √(12))/(2)$

$x=(6\pm 2√(3))/(2)$

$x=3\pm √(3)$

x=3+1.73, 3-1.73

x=4.73, 1.27

The approximate values of the non-integral roots of the polynomial equation are 4.73 and 1.27.

Therefore, the correct options are 4 and 5.