If $1, 1, \alpha$ are the roots of $x^3 - 6x^2 + 9x - 4 = 0$, then find $\alpha$.

If 1, 1, α are the roots of x³ - 6x² + 9x - 4 = 0, – Class 12 Mathematics

Question 14 of 16

1, 1, \alpha

Yanam BieapBIEAP Intermediate Board 2022Subjective· 2mImportance★★★★★

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$\alpha = 4$ .

For $x^3-6x^2+9x-4=0$ with roots $1,1,\alpha$ , the sum of the roots equals $-\dfrac{\text{coeff of }x^2}{\text{coeff of }x^3}=6$ .

So $1+1+\alpha = 6 \Rightarrow \alpha = 4$ .

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