Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i)r - 2x -8 (ii) 4s2 - 4s +1 (iii) 6r-3-7x (iv) 41+8u (v) - 15 (vi) 3r-x-4
Answers
Answer:
sorry I don't know answer
:
(1) x² - 2x -8
x² - 4x + 2x - 8
x(x-4).+2(x-4)
(x+2)(x-4)=0
x = -2 and 4
verification
sum of zeroes(α+β) = -b/a
-2 + 4 = -(-2)/1
2 = 2
product of zeroes (αβ) = c/a
-2 × 4 = -8/1
-8 = -8
(2) 4s² - 4s + 1
4s² -2s -2s +1
2s(2s - 1).-1(2s - 1)
(2s - 1)(2s - 1)
s = 1/2 and 1/2
verification
α+β = -b/a
1/2 + 1/2 = -(-4)/4
2/2 = 4/4
1 = 1
αβ = c/a
1/2 × 1/2 = 1/4
1/4 = 1/4
(3) 6x² -7x -3
6x² - 9x + 2x - 3
3x(2x-3).+1(2x-3)
(3x + 1)(2x-3) = 0
x = -1/3 and 3/2
verification
α + β = -b/a
-1/3 + 3/2 = -(-7)/6
(-2+9)/6 = 7/6
7/6 = 7/6
αβ = c/a
-1/3 × 3/2 = -3/6
-1/2 = -1/2
(4) 4u² + 8u
4u(u+2) = 0
u = 0 and -2
verification
α + β = -b/a
o + (-2) = -8/4
-2 = -2
αβ = c/a
0 × (-2) = 0/4
0 = 0
(5) t² - 15 = 0
t² = 15
t = ±√15
t = +√15 , -√15
verification
α + β = -b/a
-√15 + √15 = 0/1
0 = 0
αβ = c/a
(-√15) × (√15) = -15/1
-15 = -15
(6) 3x² - x - 4
3x² -4x + 3x - 4
x(3x-4).+1(3x-4)
(x+1)(3x-4) = 0
x = -1 , 4/3
verification
α + β = -b/a
-1 + 4/3 = -(-1)/3
(-3+4)/3 = 1/3
1/3 = 1/3
αβ = c/a
-1 × 4/3 = -4/3
-4/3 = -4/3