Question

if a and b are the roots of the quadratic equation x^2+√2x+3=0,from the quadratic polynomial with zeros 1/a,1/b​

Answer 1

Answer:

$a + b = - \sqrt{2}$

$a b = 3$

$when \: root \: are \: \frac{1}{a} \: and \frac{1}{b \: } then \: polynomial \:$

$p(x) = {x}^{2} + ( \frac{1}{a} + \frac{1}{b} )x + \frac{1}{a} \times \frac{1}{b}$

$= {x}^{2} + \frac{a + b}{ab} x + \frac{1}{ab}$

$= {x}^{2} - \frac{ \sqrt{2} }{3} x + \frac{1}{3}$

$\frac{1}{3} (3 {x}^{2} - \sqrt{2} x + 1)$