Question

3 Find the quadratic equation whose roots are √5 and -√5​

Answer 1

first ,

$\alpha + \beta = \sqrt{5} - \sqrt{5} = 0$

then ,

$\alpha \beta = - ( \sqrt{5} )( \sqrt{5} ) = - 5$

so , the Quadratic polynomial

x² + (0)x - (-5)

$\red{ \colorbox{pink}{final \: \: \: answer}}$

⇒ x² + 5

Answer 2

α+β=5−5=0

then ,

\alpha \beta = - ( \sqrt{5} )( \sqrt{5} ) = - 5αβ=−(5)(5)=−5

so , the Quadratic polynomial

x² + (0)x - (-5)