Question

Find the zeroes of the polynomial 3x²-x-4 and verify the
relationship between Zeroes and co-efficients.​

Answer 1

Step-by-step explanation:

Given polynomial is 3x² - x - 4.

So,

⇒ 3x² - x - 4

⇒ 3x² - 4x + 3x - 4

⇒ x(3x - 4) + 1 (3x - 4)

⇒ (3x - 4) (x + 1)

Zeros :

• 3x - 4 = 0

⇒ 3x = 4

⇒ x = 4/3

• x + 1 = 0

⇒ x = -1

Thus,

Zero's of polynomial are 4/3 and -1.

Now,

Sum of zeros = α + β

⇒ 4/3 + -1

⇒ [4 + (-3)]/3

⇒ 1/3

⇒ b/a

Product of zeros = αβ

⇒ 4/3 × (-1)

⇒ -4/3

⇒ c/a

This verify the relation!!

Answer 2

Given :-

3x² - x - 4

To Find :-

Find the zeroes and verify the relationship

Solution :-

3x² - x - 4

3x² - (4x - 3x) - 4

3x² - 4x + 3x - 4

x(3x - 4) + 1(3x - 4)

(3x - 4)(x + 1)

Either

3x - 4 = 0

3x = 4

x = 4/3

or

x + 1 = 0

x = 0 - 1

x = -1

Zeroes = 4/3,-1

Now

Sum of zeroes = -b/a

4/3 + (-1) = -(-1)/3

4/3 - 1 = 1/3

4 - 3/3 = 1/3

1/3 = 1/3

Product of zeroes = c/a

4/3/-1 = -4/3

4/3 × -1 = -4/3

-4/3 = -4/3