Question

Find the root of the polynomial f(x) = 2x^3 +x^2-2x-1

Answer 1

Question:

Find the zeros of the polynomial

f(x) = 2x^3 + x^2 - 2x - 1.

Answer:

x = ±1 , -1/2

Note:

• To find the zeros of a polynomial p(x) , equate it to zero. ie; Operate on p(x) = 0.

• The maximum number of zeros of a polynomial is equal to its degree.

• The cubic polynomial is of degree 3 , hence it will have maximum three zeros.

Solution:

Here,

The given polynomial is;

f(x) = 2x^3 + x^2 - 2x - 1.

Thus,

To find the zeros of given polynomial f(x) , operate on f(x) = 0.

=> 2x^3 + x^2 - 2x - 1 = 0

=> x^2(2x + 1) - (2x + 1) = 0

=> (2x + 1)(x^2 - 1) = 0

=> (2x + 1)(x + 1)(x - 1) = 0

EITHER (2x + 1) = 0

OR (x + 1) = 0

OR (x - 1) = 0

Case1 :

=> (2x + 1) = 0

=> 2x = - 1

=> x = -1/2

Case2 :

=> (x + 1) = 0

=> x = -1

Case3 :

=> (x - 1) = 0

=> x = 1

Hence,

The zeros of the given polynomial f(x) are :

x = ±1 , -1/2 .

Answer 2

$\huge{\underline{\underline{\red{\mathbf{Answer :}}}}}$

$\Large{\underline{\bf{Given :}}}$

f(x) = 2x³ + x² - 2x - 1

_______________________

$\Large{\underline{\bf{To \: Find :}}}$

We have to find the zeroes of the polynomial.

_______________________

$\Large{\underline{\bf{Solution :}}}$

To Find the zeroes, we have to operate f(x) = 0

So, A.T.Q

2x³ + x² - 2x - 1 = 0

(Taking Common Factors)

x²(2x + 1) - (2x - 1) = 0

(x² - 1) (2x - 1) = 0

★ Using Identity

$\large{\boxed{\purple{\sf{a^2 - b^2 = (a + b)(a - b)}}}}$

(Putting Values)

(x + 1)(x - 1)(2x - 1) = 0

$\rule{200}{2}$

So, x can be :

x - 1 = 0

x = 1

$\rule{150}{2}$

Or

x + 1 = 0

x = -1

$\rule{150}{2}$

Or

2x - 1 = 0

2x = 1

x = 1/2

$\large{\boxed{\pink{\sf{x = 1 \: or \: -1 \: or \: \frac{1}{2}}}}}$

$\rule{200}{2}$

#answerwithquality

#BAL