Question

If the roots of
${x}^{2} + x - k = 0$
may be the square of the other.
Find k.​

Answer 1

Heya manu ❤

$\huge {\underline {\underline {\mathtt {\blue {Answer:-}}}}}$

$let\: the\: two \:roots \:be\: m \:and \: m^2$

From the equation

a = 1

b = 1

c = -k

sum of roots = -b/a = -1

=> m+m^2=-1

=>m^2= -1-m

product of the roots = c/a = -k

=> m^3 = -k

m^3 = m(m^2)

= m(-1-m)

=> -k = -m-m^2

=> -k = -m-(-1-m)

=> -k = -m+1+m

=> -k = 1

=> k = -1

Answer 2

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