Alfredo Holmes
2022-03-28
Answered

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Luciana Cline

Answered 2022-03-29
Author has **14** answers

Step 1

Your determinant value seems to be wrong. The correct determinant is

$-{\alpha}^{2}{p}^{2}r+{\alpha}^{2}p{q}^{2}-2\u200a\alpha pqr+2\u200a\alpha {q}^{3}-p{r}^{2}+{q}^{2}r$

$=-(pr-{q}^{2})({\alpha}^{2}p+2\u200aq\alpha +r)$

so unless $pr={q}^{2},\text{}\alpha$ is indeed a root of $p{x}^{2}+2qx+r$

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