Question

If 3 is a zero of the polynomial 2x 3 - x 2 – 13x -6 , then other zeroes are a) 2 , 1/2 b) – 2 ,-1/2 c) 2 , -1/2 d) – 2 , 1/2​

Answer 1

Putting x=3

2×3

3

−3

2

−13×3−6=0

Hence, 3 is zero of this polynomial

it's your answer

Answer 2

(b) - 2 , -1/2

Step-by-step explanation:

CORRECT QUESTION :-

If 3 is a zero of the polynomial 2x³ - x² - 13x - 6, Then other zeroes are

a) 2 , 1/2 b) -2 , -1/2

c) 2 , -1/2 d) - 2 , 1/2

_____________________

SOLUTION :-

Given that,

3 is a zero of polynomial.

=> x = 3

=> x - 3 = 0...(1)

Now,

divide (1) from the polynomial.

=>

2x² + 5x + 2

x-3 ) 2x³ - x² - 13x - 6

– 2x³ - 6x²

- +

5x² - 13x

– 5x² - 15x

- +

2x - 6

– 2x - 6

- +

0

_____________________

Now,

The Quotient is -

2x² + 5x + 2

So,

2x² + 5x + 2 = 0

=> 2x² + 4x + x + 2 = 0

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

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

So,

Zeroes are -

x + 2 = 0

=> x = -2

And,

2x + 1 = 0

=> 2x = - 1

=> x = -1/2

So,

The other two zeroes are - 2 , - 1/2 (b)

And,

Total zeroes are,

- 2 , -1/2 , 3

_______________________

Hope it helps.

#BeBrainly :-)