POLYNOMIALS
EXERCISE 2.2
1. Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
(1) x2 - 2x - 8
(ii) 482-45+1
(m) 6 -3-7x
Answers
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(1) x2-2x-8
x2-4x+2x-8
=x(x-4)+2(x-4)
=(x-4) (x+2)
x-4=0 x+2=0
x=4 x=-2
alpha=4,beta= -2
alpha +beta = -b/a
4+(-2)=-(-2)/1
4-2=2/1
2=2
alpha×beta=c/a
4×-2=-8/1
-8=-8
(2) 4s2-4s+1
=4s2- -2s+ -2s+1
=2s(2s-1)-1(2s-1)
=(2s-1)(2s-1)
=2s-1=0
s=1/2
alpha=1/2 beta=1/2
alpha+beta=-b/a
1/2+1/2=-(-4)/4
1=4/4
1=1
alpha×beta=c/a
1/2×1/2=1/4
1/4=1/4
x2-4x+2x-8
=x(x-4)+2(x-4)
=(x-4) (x+2)
x-4=0 x+2=0
x=4 x=-2
alpha=4,beta= -2
alpha +beta = -b/a
4+(-2)=-(-2)/1
4-2=2/1
2=2
alpha×beta=c/a
4×-2=-8/1
-8=-8
(2) 4s2-4s+1
=4s2- -2s+ -2s+1
=2s(2s-1)-1(2s-1)
=(2s-1)(2s-1)
=2s-1=0
s=1/2
alpha=1/2 beta=1/2
alpha+beta=-b/a
1/2+1/2=-(-4)/4
1=4/4
1=1
alpha×beta=c/a
1/2×1/2=1/4
1/4=1/4
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