Question

Obtain the zeros of the quadratic poly nomial √3x²-8x+4√3 and verify the relationship between its zeros and coefficients

Answer 1

Hey mate step by step explanation

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Answer 2

Answer:

The zeroes of the polynomial are 2/√3 and 2√3.

Step-by-step explanation:

The zeroes of a quadratic polynomial are the numbers which satisfy the given equation, means they when put in the equation will result the value to zero.

Here, the given quadratic polynomial is

√3${x}^{2}$ - 8x +4√3

To find the zeroes,

We must equate the polynomial to 0 making it an equation.

so, the required equation is,

√3${x}^{2}$ - 8x + 4√3 = 0

=> √3${x}^{2}$ - 6x - 2x + 4√3 =0

taking the commons and factorising,

we get,

=> √3x ( x - 2√3 ) - 2 ( x - 2√3 ) =0

=> (x - 2√3 )(√3x -2 ) = 0

=> (x - 2√3 )= 0 and (√3x -2 ) = 0

=> x = 2√3 and x = 2/√3

so, the zeroes of this polynomial are

2√3 and 2/√3

Now, here in the quadratic polynomial, the coefficients....

a = √3

b = -8

and the constant term,

c = 4√3

Verification :

we know that

sum of zeroes

= -( coefficient of x/ coefficient of ${x}^{2}$ )

= - b/a

= -( -8/√3 )

= +8/√3

= 2/√3 + 2√3 ( the sum of zeroes )

now,

product of zeroes

= ( constant term/ coefficient of ${x}^{2}$ )

= c/a

= 4√3/√3

= 4

= 2/√3 × 2√3 ( the product of zeroes)

Hence, Verified.