Question

5x-4√3+2√3x² verify the relation between zeros​

Answer 1

Answer:

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Step-by-step explanation:

Firstly factorise the given polynomial and then put each factor equal to zero to find required zeroes and then for verification show that

Sum of zeroes = - coefficient of x/coefficient of x²

Product of zeroes = constant term/coefficient of x²

SOLUTION:

Let p(x) = 4√3x² +5x -2√3

4√3x² +8x -3x -2√3

[By splitting the middle term]

4x (√3x +2) - √3(√3x +2)

(4x-√3) (√3x +2)

To find zeros, put p(x)= 0

(4x-√3)= 0 or  (√3x +2)= 0

4x = √3    or √3x = -2

x= √3/4   or x = -2/√3

Hence, zeroes of the polynomial are √3/4 and -2/√3.

Verification:

Sum of zeroes = (√3/4) +(-2/√3)

- coefficient of x/coefficient of x² =√3/4 -2/√3

- 5/4√3 = (√3×√3)-(2×4)/4√3

-5/4√3 =(3-8)/4√3

- 5/4√3 =-5/4√3

Product of zeroes = (√3/4) (-2/√3)= -½

constant term/coefficient of x² = -½

-2√3/ 4√3 = -½

-½ = -½

So, the relationship between the zeroes and its coefficients is verified.

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