Question

the roots of quadratic equation ax^2+bx +c=0 are alpha and beta then whose equation roots are alpha square and beta square

Answer 1

Answer:

$\\ {a}^{2} {x}^{2} - ( {b}^{2} - 2 {a}^{3}b )x + {c}^{2} = 0$

Step-by-step explanation:

$\alpha + \beta = - \frac{b}{a} \\ \\ \alpha \beta = \frac{c}{a} \\ \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ \\ = \frac{ {b}^{2} }{ {a}^{2} } - 2ab \\ \\ {( \alpha \beta )}^{2} = \frac{ {c}^{2} }{ {a}^{2} } \\ \\ required \: equation \: \\ \\ {x}^{2} - ( { \alpha }^{2} + { \beta }^{2} )x + { \alpha }^{2} { \beta }^{2} = 0 \\ \\ {x}^{2} - ( \frac{ {b}^{2} - 2 {a}^{3} b}{ {a}^{2} } )x + \frac{ {c}^{2} }{ {a}^{2} } = 0 \\ \\ \\ \\ {a}^{2} {x}^{2} - {(b}^{2} - 2 {a}^{3} b)x+ {c}^{2} = 0 \\ \\ {a}^{2} {x}^{2} - ( {b}^{2} - 2 {a}^{3}b )x + {c}^{2} = 0$