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The product of uncommon real roots of th...

The product of uncommon real roots of the polynomials ` p(x)=x^4+2x^3-8x^2-6x+15` and ` q(x) ` `= x^3+4x^2-x-10 ` is :

A

`-6`

B

`-5`

C

`5`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Let `alpha` be the common root.
`:.alpha^(4)+2alpha^(3)-8alpha^(2)-6alpha+15=0`
`alpha^(3)+4alpha^(2)-alpha-10=0`
`:.` Given equations are
`(alpha^(2)-3)(alpha^(2)+2alpha-5)=0` and `(alpha+2)(alpha^(2)+2alpha-5)=0`
`implies` For common roots, `alpha^(2)+2alpha-5=0`
`:.` Product of uncommon real roots is `(-3)(-2)=6`
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