EXERCISE - 3.3
Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
(i) x2 - 2x - 8
(ii) 4.s2 -- 4s + 1
(iii) 6x2 – 3-7x
(iv) 4u2 + 8u
(v) † - 15
(vi) 3x2 - x - 4
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Step-by-step explanation:
i) x²-2x-8 = x²+2x-4x-8 = x(x+2) -4(x+2) = (x-4)(x+2)
(x-4) = 0 (x+2) = 0
x = 4 x = -2
Zeroes = 4,-2
ii) 4s²-4s+1 =4s²-2s-2s+1 = 2s(2s-1) -1(2s-1) = (2s-1)(2s-1)
2s-1 = 0
2s = 1
s = 1/2
Zero = 1/2
iii) 6x²-7x-3 = 6x²+2x-9x-3 = 2x(3x+1) -3(3x+1) = (2x-3)(3x+1)
2x-3 = 0 3x+1 = 0
x = 3/2 x = -1/3
Zeroes = 3/2, -1/3
iv)4u²+8u = (4u)(u+2)
u+2 = 0 4u = 0
u = -2 u = 0
Zeroes = -2, 0
vi) 3x²-x-4 = 3x²+3x-4x-4 = 3x(x+1) -4(x+1) = (3x-4)(x+1)
3x-4 = 0 x+1 = 0
x = 4/3 x = -1
Zeroes = 4/3, -1
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