4. The roots of the equation x
2 + 6x + q = 0 are α and α − 1. Find the value of q
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Step-by-step explanation:
ANSWER
Consider the equation x
2
−6x+q=0, where a = 1, b = -6, c = q
(i) Sum of the roots m+n=
a
−b
=
1
−(−6)
∴m+n=6
(ii) Product of the roots mn=
a
c
=
1
q
∴mn=q
If one root is m then twice the root is 2m.
∴m=m and n=2m
m+n=6∴m+2m=6,3m=6∴m=
3
6
=2
We know that q=mn∴q=m(2m)=2m
2
=2(2)
2
=8∴q=8
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