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If we are having a cubic equation with two equal and real roots . For ex- ax^3-9x^2+12x-5. Then what all conditions we can impose to get all values of 'a'. Also how can we find the given roots.
Help me with it experts....

Santosh Rao , 8 Years ago
Grade
anser 1 Answers
ANIKET RAJ
a cubic equation is in the form:----
ax3-(\alpha+β+γ)x2+(\alphaβ+βγ+γ\alpha)-\alphaβγ
let equal root be \alpha,then equation ,
ax3-(\alpha+\alpha+γ)x2+(\alpha\alpha+\alphaγ+γ\alpha)-\alpha\alpha
from equation given,,
2\alpha+γ=9/a.........................(2)
\alpha2+2\alphaγ=12/a
\alpha2γ=5/a..........................(1)
from above eq.
\alpha2=5/aγ and put this value in(2)
and solve
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Last Activity: 8 Years ago
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