Question

x^3+8x^2-5x-84=0,find the roots?​

Answer 1

Answer:

Here x = 3 is one root of equation ( Hit & trial method)

so (x - 3) is a factor of polynomial.

now,

${x}^{3} - 3 {x}^{2} + 11 {x}^{2} - 33x + 28x - 84 = 0$

${x}^{2} (x - 3) + 11x(x - 3) + 28(x - 3) = 0$

$(x - 3)( {x}^{2} + 11x + 28) = 0$

$(x - 3)( {x}^{2} + 7x + 4x + 28) = 0$

$(x - 3)( x(x + 7) + 4(x + 7)) = 0$

$(x - 3)(x + 7)(x + 4) = 0$

so roots are X = 3, -7, -4 Ans