Question

find the condition that one root of x^2+px+q=0 is the square of other.

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Answer 1

Step-by-step explanation:

ANSWER:

$let \: the \: roots \: be \: \alpha \: { \alpha }^{2}$

$the \: sum \: of \: roots \: = \alpha + { \alpha }^{2} = - p ... eq1\\ product \: ofroots \: = q = { \alpha }^{3} ...eq2\\ then \: \alpha = \sqrt[3]{q} ...eq3\\ substitute \: eq3 \: in \: eq1 \\ \alpha (1 + \alpha ) = - p \\ \sqrt[3]{q} (1 + \sqrt[3]{q} ) = - p \\ hence \: this \: the \: condtion$