Question

find the sum and product of zeroes of the polynomial 3x2-x-4​

Answer 1

Topic :-

Zeroes of the Polynomial

Given :-

3x² - x - 4

To Find :-

Sum and Product of zeroes of given polynomial.

Solution :-

Firstly, we will find zeroes of the polynomial and then we will add and multiply them to find the sum and product of the zeroes respectively. To find zeroes of the polynomial we will equate given equation with zero.

3x² - x - 4 = 0

Splitting x into 4x and -3x,

3x² - (4x - 3x) - 4 = 0

Opening brackets,

3x² - 4x + 3x - 4 = 0

Rearranging it,

3x² + 3x - 4x - 4 = 0

Taking 3x as common from first two terms,

3x(x + 1) - 4x - 4 = 0

Taking -4x as common from last two terms,

3x(x + 1) - 4(x + 1) = 0

Taking (x + 1) as common from the expression,

(x + 1)(3x - 4) = 0

Now,

Either (x + 1) = 0 or

(3x - 4) = 0

Taking Case 1,

x + 1 = 0

x = -1

Taking Case 2,

3x - 4 = 0

3x = 4

x = 4/3

Hence, x = -1 and x = 4/3 are zeroes of the given polynomial.

Calculating sum of zeroes,

-1 + (4/3)

(-1(3) + 4)/3

(-3 + 4)/3

1/3

Calculating product of zeroes,

-1 × (4/3)

(-1(4))/3

-4/3

Answer :-

So, the sum of zeroes of the given expression is 1/3 and the product of zeroes of the given expression is -4/3.

Answer 2

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