Question

Solve the polynomial (STEP BY STEP)

(X+1)(X^2-5X+10) = 12

Ans is (1,1,2)

#salute u if u solved it

Answer 1

p(X) = (X+1) (X^2-5X+10) = 12

X^3 - 5X^2 + 10X + X^2-5X+10 = 12

X^3 - 4X^2 + 5X + 10 = 12

X^3 - 4X^2 + 5X = 12 - 10

X^3 - 4X^2 + 5X = 2

X^3 - 4X^2 + 5X - 2 = 0

Now,

Factors of 2 : 1,2

By putting x = 1, we have p(1) = 0

Therefore, (X - 1) is a factor of P(X)

By dividing (X - 1) by P(X) by long-division method we have

(X^2 - 3X + 2)

= (X -1) (X^2 - 3X + 2)

= (X -1) (x^2 - 2X - X + 2)

= (X -1) 【 X (X-2) -1(X - 2)】

= (X -1) 【 (X - 1) ( X - 2)】

= (X -1) (X -1) (X -2)

Ans : 1,1,2