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obtain the zeroes of the polynomial √3x square - 8x +4√3 and verify the relation between the zeroes and coefficients ..
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obtain the zeroes of the polynomial √3x square - 8x +4√3 and verify th...
Finding the Zeroes of the Polynomial:
• The given polynomial is √3x^2 - 8x + 4√3.
• To find the zeroes, we need to set the polynomial equal to zero and solve for x.
• √3x^2 - 8x + 4√3 = 0.
• To simplify, let's substitute y = x√3.
• This gives us y^2 - 8y + 12 = 0.
• Factoring the quadratic equation, we get (y - 6)(y - 2) = 0.
• Therefore, y = 6 or y = 2.
• Substituting back y = x√3:
• x√3 = 6 or x√3 = 2.
• This gives us x = 2/√3 or x = 6/√3.
• Simplifying further, we get x = 2√3 or x = 6√3.
Verifying the Relation Between Zeroes and Coefficients:
• The sum of the zeroes is given by x1 + x2 = 2√3 + 6√3 = 8√3.
• The product of the zeroes is given by x1 * x2 = 2√3 * 6√3 = 12.
• By Vieta's formulas, the sum of the zeroes is related to the coefficients of the polynomial.
• The sum of the zeroes = -(-8) / √3 = 8√3 (as expected).
• The product of the zeroes = 4√3 (as expected).
Therefore, the relation between the zeroes and coefficients of the polynomial √3x^2 - 8x + 4√3 is verified through calculations and Vieta's formulas.
• The given polynomial is √3x^2 - 8x + 4√3.
• To find the zeroes, we need to set the polynomial equal to zero and solve for x.
• √3x^2 - 8x + 4√3 = 0.
• To simplify, let's substitute y = x√3.
• This gives us y^2 - 8y + 12 = 0.
• Factoring the quadratic equation, we get (y - 6)(y - 2) = 0.
• Therefore, y = 6 or y = 2.
• Substituting back y = x√3:
• x√3 = 6 or x√3 = 2.
• This gives us x = 2/√3 or x = 6/√3.
• Simplifying further, we get x = 2√3 or x = 6√3.
Verifying the Relation Between Zeroes and Coefficients:
• The sum of the zeroes is given by x1 + x2 = 2√3 + 6√3 = 8√3.
• The product of the zeroes is given by x1 * x2 = 2√3 * 6√3 = 12.
• By Vieta's formulas, the sum of the zeroes is related to the coefficients of the polynomial.
• The sum of the zeroes = -(-8) / √3 = 8√3 (as expected).
• The product of the zeroes = 4√3 (as expected).
Therefore, the relation between the zeroes and coefficients of the polynomial √3x^2 - 8x + 4√3 is verified through calculations and Vieta's formulas.
Community Answer
obtain the zeroes of the polynomial √3x square - 8x +4√3 and verify th...
Let f(x) = √3x2+ 8x + 4√3√3x2+ 8x + 4√3 = 0√3x2+ 6x + 2x + 4√3 = 0√3x(x + 2√3) + 2(x + 2√3) = 0(x + 2√3)(√3x + 2) = 0x + 2√3 = 0 or √3x + 2 = 0x = -2√3 or x = -2/√3So, the zeroes of √3x2+ 8x + 4√3 are -2√3 and -2/√3
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