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4√3x²+5x-2√3find the zeros of the following quadratic polynomials and verify the realtion between the zeros and the co-efficients |
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Answer» 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 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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