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Question

f(x).g(x)=0 where f(x) and g(x) are degree 2 polynomial with some of zeroes -2 and +2 respectivily.These constant term is same as well as coefficient of highest degree term. Then number of coincident zeroes of there product is

A
1
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B
2
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C
3
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D
None of these
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Solution

The correct option is D None of these
f(x)=ax2+bx+cg(x)=ax2+bx+c
f(x)g(x)=(ax2+bx+c)(ax2+bc+c)
0=(x2+bxa+ca)(x2+bax+ca)
o=(x2(α+β)x+αβ)(x2(δ+γ)x+δγ)
o=(xα)(xβ)(xδ)(xγ)
x=α,β,δ,γ
where α,β are zeroes of f(x) δγ are zeroes of g(x)
so all zeroes coincide with f(x)g(x)

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