find the zeroes of polynomial p(x)=4 root over 3x^2 plus 5x minus 2 root over 3 and verify the relationship between zeroes and its co-efficient.
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Answer:
mark brainliest
Step-by-step explanation:
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
Hence sum of the roots =-b/a.
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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