42) If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}+x-4=0 \) form the quadratic equation whose roots are \( \alpha^{2} \) and \( \beta^{2} \).

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42) If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}+x-4=0 \) form the quadratic equation whose roots are \( \alpha^{2} \) and \( \beta^{2} \).

) 42) If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}+x-4=0 \) form the quadratic equation whose roots are \( \alpha^{2} \) and \( \beta^{2} \).

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

given-:

a+b=-1............ eqn ¹

ab=-4. ............. eqn ²

on squaring eqn ¹

a²+b²+2ab=1

a²+b²=9

on squaring eqn ²

a²b²=16

hence the eqn is

x²+9x+16=0

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42) If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}+x-4=0 \) form the quadratic equation whose roots are \( \alpha^{2} \) and \( \beta^{2} \).

1 Answers