A and B are zeroes of the quadratic polynomial
f(x) = x2 – 6x + y. Find the value of ‘y’ if 3a + 2b = 20.
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Thus y = 8 or -72
Step-by-step explanation:
f(x) = x² – 6x + y
A and B are zeros of f(x)
so F(A)=0 and f(B)=0
A²-6A+y=0............(1)
and
B²-6B+y=0..............(2)
on subtration we get
A²-B²-6(A-B)=0
(A-B)( A+B-6)=0
A=B or A+B+6
also 3A+2B=20
3A+2A=20
A=4,B=4
From(1) 16-24+y=0
y=8
If A+B+6=0
3A+2*(-A-6)=0
3A-2A-12=0
A=12
B=-6-12=-18
Then from (1)144-72+y=0
y=-72
Thus y=8 or -72
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