Question

2m³+m²-2m-1=0 find the roots​

Answer 1

Answer:

-1/2, -1, 1

Step-by-step explanation:

f(m) =2m³+ m²- 2m - 1

if m = -1

f(-1)= 2(-1)³ +(-1)²- 2(-1) - 1

    = -2 + 1 + 2 - 1

    = 0

Therefore m+1 is a factor of f(m) {factor theorem}

Dividing f (m)  by (m+1),

we get 2m²- m - 1

Factorising 2m²- m - 1,

2m²- (2-1)m -1

=> 2m²- 2m + m - 1

=> 2m(m-1) + 1(m-1)

=> (2m+1)(m-1)

Thus factors are (2m+1), (m-1), (m+1)

The roots are -1/2, 1 and -1