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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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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