Question

If a, b, c are the roots of the equation $x^3+2x^2+1=0$ . Find the equation whose roots are b + c - a,c + a - b, a + b - c.

• A. +
• B. + 2
• C. + 2
• D. +

Answer 1

The correct option is B

+ 2

$x^3$ + 2 $x^2$ + 1 = 0 __________(1)

a + b + c = -2

(a + b + c) - 2a = -2 - 2a

b + c - a = - 2 - 2a

Lets one root is y

y = - 2 - 2a

- $\frac{(y+2)}{2}=a$

Since a is the roots of the equation $x^3$ + 2 $x^2$ + 1 = 0

We can replace a by x to generalize it.

- $\frac{(y+2)}{2}$ = x

Replace x in terms of y in equation 1

$-\frac{(y+2{)}^3}{8}+2\frac{(y+2{)}^2}{4}+1=0$

-( $y^3$ + 8 + 6 $y^2$ + 12y) + 4( $y^2$ + 2y + 4) + 1 = 0

- $y^3$ - 2 $y^2$ - 4y - 9 = 0 $y^3$ + 2 $y^2$ + 4y + 9 = 0

Write the equation in terms of x

$x^3$ + 2 $x^2$ + 4x + 9 = 0.