Question

2. Find a quadratic polynomial whose zeroes are
$\sqrt{2 \: } \: \:and \: \: \frac{2}{5}$
​

Answer 1

Answer:

α = √2

β = $\frac{2}{5}$

Required Quadratic Polynomial = 5x² - 5√2x + 2

Answer 2

$\sf\bold{\underline{\pink{SOLUTION}}}$

α $\sf{= \sqrt{2}}$

β $\sf{= \dfrac{2}{5}}$

α + β $\sf\bold\blue{= \dfrac{5\sqrt{2} + 2}{5}}$

α.β $\sf\bold\blue{= \dfrac{2\sqrt{2}}{5}}$

$\sf\bold{\underline{\pink{Quadratic\: Polynomial}}}$

$\sf{→ x² - (α+β)x + (α.β)}$

$\sf{→ x² - (\dfrac{5\sqrt{2} + 2}{5} ) + (\dfrac{2\sqrt{2}}{5})}$

$\sf{→ \dfrac{5x² - (5\sqrt{2} + 2)x + 2\sqrt{2}}{5}}$