Question

10. If two zeroes of the polynomial
$(2x {}^{3} - 4x - x {}^{2} + 2) \: are \: \sqrt{2} \: and \\ - \sqrt{2} , then \: obtain \: the \: third \: zero.$


Standard:- 10

Content Quality Solution Required


❎ Don't Spamming❎

Answer 1

Hope it's help you friend ☺️

Answer 2

^_^ Other Method •_^
Final Answer : Third zero is 1/2

Steps:
1) We know that,
Product of roots of
$a {x}^{3} + b {x}^{2} + cx + d = 0$
is
$\frac{ - d}{a}$

In
$2 {x}^{3} - {x}^{2} - 4x + 2 = 0 \\ a = 2 \: and \: d \: = 2$
2)We have,
Let the third zero be ¥.
Product of roots = -d/a
$= > \sqrt{2} \times (- \sqrt{2} ) \times \gamma = \frac{ - 2}{2} \\ = > - 2 \times \gamma = - 1 \\ = > \gamma = \frac{1}{2}$

Hence, Third zero is 1/2 .