Question

If two roots of x ^ 3 + 3x² - 9x + c = 0 are
9x + c = 0 are equal, then find the value of c.​

Answer 1

Step-by-step explanation:

Given equation is

${x}^{3 } + 3 {x}^{2} - 9x + c = 0$

for equal roots

let the two equal roots have value = "a"

then( x-a)^2 divide the given equation and remainder = zero

therefore

(x-a)^2 = x^2 - 2ax + a^2

x(x^2 - 2ax + a^2) = x^3 - 2ax^2 + a^2x

after subtracting it from the given equation, we get

(3+2a)x^2 + (-9-a^2)x + c

now again from the above equation subtracting the

(3+2a) (x^2 - 2ax + a^2)

then we get

(-9-a^2+6a+4a^2)x + ( c-3a^2-2a^3) =0

==}. a^2+2a-3= 0. ; 2a^3+3a^2-c=0