Question

Find the zeroes of the polynomial p (x)= 4 root 3 x^2 -2 root 3 x -2 root 3 .Verify the relationship between the zeroes and coefficient .​

Answer 1

Given Equation:-

• 4√3x² - 2√3x - 2√3

To Find:-

• The zeroes of the polynomial
• Verify the relationship between the zeroes and coefficient

Solution:-

The given equation is 4√3x² - 2√3x - 2√3

Let us find the zeroes using the splitting the middle term method.

• 4√3x² - 2√3x - 2√3

Let us split the middle term:-

4√3x² - 4√3x + 2√3x - 2√3

Taking common:-

4√3x(x - 1) + 2√3(x - 1)

Taking common terms together:-

(x - 1)(4√3x + 2√3)

Now,

Either,

x - 1 = 0

=> x = 1

Or,

4√3x + 2√3 = 0

=> 4√3x = -2√3

=> x = -2√3/4√3

=> x = -1/2

Therefore the two zeroes of the polynomial are 1 and -1/2

Let us verify the relationship between zeroes and coefficient,

We know,

Sum of zeroes = -(Coefficient of x)/(Coefficient of x²)

Hence,

1 + (-1/2) = -(-2√3)(4√3)

= (2 - 1)/2 = 2√3/4√3

=> 1/2 = 1/2

Also we know,

Product of zeroes = (Constant Term)/(Coefficient of x²)

Hence,

1 × (-1/2) = -2√3/4√3

=> -1/2 = -1/2

Hence Verified!!!

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Answer 2

Answer:

Let us find the zeroes using the splitting

the middle term method.

4V3x2 - 2-V3x - 2v3

Let us split the middle term:

4V3x2 - 4v3x + 2v3x - 2v3

Taking common:

4V3x(x - 1) + 2/3(x - 1)

Taking common terms together:

(x - 1)(473x + 2/3)

Now,

Either,

X-1 = 0

=> x= 1

Or,

4V3x + 2 v 3 = 0

=> 4V3x = -2V3

=> x=-273/473

=> x = -1/2

Therefore the two zeroes of the polynomial are 1 and -1/2

Let us verify the relationship between zeroes and coefficient,

We know,

Sum of zeroes = -(Coefficient of x)/ = (Coefficient of x')

Hence,

1 + (-1/2) = -(-23)(413) = (2 1)/2 = 213/4v3

=> 1/2 = 1/2

Also we know,

Product of zeroes = (Constant Term)/ = (Coefficient of x²)

Hence,

1 * (-1/2) = -2v3/4v3

=> -1/2 = -1/2

Hence prooved..