Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and their coefficient.
1) 6x² -3-7x (2 marks)
2) 5n^2 - 25n (3 marks)
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Answer:
1. 6x^2 -3 -7x
Solution:
6x^2 -7x -3
= 6x^2- (9-2)x -3
=6x^2 - 9x +2x -3
=3x (2x -3) +1 (2x -3)
= (2x -3)(3x+1)
p (x) =0
(2x-3)(3x+1)=0
Either or
2x-3=0 3x+1=0
x=3/2 x= -1/3
Verification:
sum of the zeroes = -b/a
3/2+(-1/3)= - (-7)/6
9-2/6 = 7/6
7/6=7/6
Hence proved
2.5n^2 - 25n
Solution:
5n ( n - 5)
p (x)=0
5n (n-5)=0
Either or
5n=0 n-5=0
n=0 n=5
Verification:
sum of the zeroes = -b/a
0+5 = - (-25/5)
5=5
Hence proved
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