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Algebra

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 agoGrade

1 Answer

ANIKET RAJ

Approved Tutor Answer8 Years ago

a cubic equation is in the form:----

ax³-( $\alpha$ +β+γ)x²+( $\alpha$ β+βγ+γ $\alpha$ )- $\alpha$ βγ

let equal root be $\alpha$ ,then equation ,

ax³-( $\alpha$ + $\alpha$ +γ)x²+( $\alpha$ $\alpha$ + $\alpha$ γ+γ $\alpha$ )- $\alpha$ $\alpha$

from equation given,,

2 $\alpha$ +γ=9/a.........................(2)

$\alpha$ ²+2 $\alpha$ γ=12/a

$\alpha$ ²γ=5/a..........................(1)

from above eq.

$\alpha$ ²=5/aγ and put this value in(2)

and solve

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