Question

Find the zeroes of the polynomial f(x) = 4√3x²+5x-2√3 , and verify the relationship between the zeroes and it's cofficients​

Answer 1

Answer:

The given polynomial f(x)

= 4√3 x^2 +5x - 2√3

= 4√3 x^2 + 8x - 3x - 2√3

= 4x(√3 x +2) - √3 (√3 x +2)

= (√3x+2)(4x-√3)

Hence the zeroes are -2/√3 and √3/4

Sum of the roots = -2/√3 + √3/4 = -2√3/3 + √3/4 = (-8√3+3√3)/12 = -5√3/12

Sum of the roots = -b/a = -5/4√3 = -5√3/12

Product of the roots = (-2/√3)(√3/4) = -1/2.

Product of the roots = c/a = -2√3/4√3 = -1/2.

So product of the roots = c/a.

Thus, the relationship between the roots and coefficients is verified.

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