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If a(1) x^(3) + b(1)x^(2) + c(1)x + d(1)...

If `a_(1) x^(3) + b_(1)x^(2) + c_(1)x + d_(1) = 0 and a_(2)x^(3) + b_(2)x^(2) + c_(2)x + d_(2) = 0`
a pair of repeated roots common, then prove that
`|{:(3a_(1)", "2b_(1) ", "c_(1)),(3a_(2)", " 2b_(2)", "c_(2)),(a_(2)""b_(1)- a_(1)b_(2)", "c_(2)a_(1)-c_(2)a_(1)", "d_(1)a_(2)-d_(2)a_(1)):}|=0`

Text Solution

AI Generated Solution

To prove that the determinant \[ \begin{vmatrix} 3a_1 & 2b_1 & c_1 \\ 3a_2 & 2b_2 & c_2 \\ a_2b_1 - a_1b_2 & a_2c_1 - a_1c_2 & a_2d_1 - a_1d_2 \end{vmatrix} = 0 ...
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