Question

Find the zers of4√3x^2+5x-2√3and verify the relation between zeros and coefficient of the polynomial

Answer 1

Question

Find the zeros of 4√3x² + 5x - 2√3 and verify the relation between zeros and coefficient of the polynomial.

Solution

Given polynomial is 4√3x² + 5x - 2√3

The above polynomial or equation is in the form ax² + bx + c which is equal to zero.

So, we can solve it my splitting the middle term or by quadratic formula.

→ 4√3x² + 5x - 2√3 = 0

→ 4√3x² + 8x - 3x - 2√3 = 0

→ 4x(√3x + 2) -√3(√3x + 2) = 0

→ (4x - √3) (√3x + 2) = 0

→ x = √3/4, -2/√3

So, the zeros of the polynomial are √3/4 and -2/√3.

Also, we have to verify the relation between zeros and coefficient of the polynomial.

Verification

Polynomial = 4√3x² + 5x - 2√3

Here, a = 4√3, b = 5 and c = -2√3

Sum of zeros = -b/a

√3/4 + (-2/√3) = -5/4√3

(3 - 8)/4√3 = -5/4√3

-5/4√3 = -5/4√3

Product of zeros = c/a

(√3/4) × (-2/√3) = -2√3/4√3

-2√3/4√3 = -2√3/4√3

-1/2 = -1/2

Answer 2

||✪✪ QUESTION ✪✪||

Find the zers of4√3x^2+5x-2√3and verify the relation between zeros and coefficient of the polynomial ?

|| ★★ FORMULA USED ★★ ||

The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

|| ✰✰ ANSWER ✰✰ ||

Before Solving The Quadratic Equation , Put This Equal to Zero.

→ 4√3x² + 5x - 2√3 = 0

Splitting The Middle Term Now,

→ 4√3x² + 8x - 3x - 2√3 = 0

→ 4x(√3x +2) -√3(√3x + 2) = 0

→ (4x - √3) (√3x + 2) = 0

Putting Both Equal to Zero now,

→ (4x - √3) = 0

→ 4x = √3

→ x = (√3/4)

And,

→ (√3x + 2) = 0

→ √3x = (-2)

→ x = (-2/√3)

So, Zeros Of The Polynomial are (√3/4) and (-2/√3) .

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Now, Relation between zeros and coefficient of the polynomial :-

For a Quadratic Equation ax² + bx + c = 0 ,

→ Product of zeroes = c/a = Constant term / (Coefficient of x²)

→ Sum of Zeroes = (-b/a) = - ( Coefficient of x ) / ( Coefficient of x²)

From Equation 4√3x² + 5x - 2√3 = 0 we have now :-

→ a = (4√3)

→ b = 5

→ c = (-2√3)

So,

→ Product of Zeros = c/a = (-2√3)/(4√3) = (-1/2)

Now, we have ,

→ Product of zeros = (√3/4) * (-2/√3) = (-1/2) Verified .

And,

→ sum of zeros = (-b/a) = (-5)/(4√3)

→ Also , sum of zeros = (√3/4) + (-2/√3) =(3-8) /(4√3) = (-5)/(4√3) Verified .

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