If the equations x2+3x+5=0 and ax2+bx+c=0;a,b,c∈N have a common root, then the least possible value of a+b+c is
A
1
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B
3
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C
5
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D
9
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Solution
The correct option is D9 x2+3x+5=0 Δ=9−20=−11<0 Thus, the above equation has imaginary roots. The coefficients are real, so the imaginary roots will be in conjugate pair.
Given x2+3x+5=0 and ax2+bx+c=0 have a common root. So, we can conclude that both the roots are common. ⇒a1=b3=c5=k(say) ⇒a+b+c=9k
But given that a,b,c∈N ∴ The minimum value of a+b+c is 9