An important and conceptual question from polynomials in which we have given a equation 4x²-4x-3 and we have to find the zeroes of the quadratic polynomials and asked to verify the relationship between the zeroes and the coefficients
RS Aggarwal, Class 10, chapter 2A, question no 4
Let f(x) = 4x²-4x-3
= 4x²-(6x-2x)-3
= 4x² – 6x + 2x – 3
= 2x (2x-3) + 1(2x-3)
= (2x + 1) (2x-3)
To find the zeroes, set f(x) = 0
(2x + 1) (2x – 3)= 0
2x + 1 = 0 or 2x – 3 = 0
x = -1/2 or x = 3/2
Again, Sum of zeroes = (-1/2) + (3/2) = (-1+3)/2 = 2/2
= -b/a
= (-Coefficient of x)/(Cofficient of x2) Product of zeroes = (-1/2)(3/2) = (-3)/4 = c/a = Constant term / Coefficient of x²