Question

Find the zero of quadratic polynomial and verify the relation between zeros and it's coefficient ( 1 ) 4s2 - 4s +1 (2.) 6x2 - 3 - 7x

Answer 1

(i) 4s2 – 4s + 1 = (2s-1)2 The value of 4s2 - 4s + 1 is zero when 2s - 1 = 0, i.e., s = 1/2 Therefore, the zeroes of 4s2 - 4s + 1 are 1/2 and 1/2.Sum of zeroes = 1/2 + 1/2 = 1 = -(-4)/4 = -(Coefficient of s)/Coefficient of s2 Product of zeroes = 1/2 × 1/2 = 1/4 = Constant term/Coefficient of s2  

(ii)6x2-3-7x = 6x2 - 7x - 3 = (3x + 1) (2x -3)

The value of 6x2 3 -7x is zero when 3x + 1 = O or 2x - 3 = 0, i.e., X = -1/3 or x = 3/2 Therefore, the zeroes of 6x2 3 7x are -1/3 and 3/2.Sum of zeroes = -1/3 + 3/2 = 7/6 = -(-7)/6 = -(Coefficient of(i) x2 - 2x - 8 = (x - 4) (x + 2) The value of x2 - 2x)/Coefficient of x2 Product of zeroes = -1/3 x 3/2 = -1/2 = -3/6 = Constant term/Coefficient of x2

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