Question

Find all the zeroes of the polynomial 8x4+8x3-18x2-20x-5 if its is given that two of its zeroes are √5/2 and -√5/2

Answer 1

Here is your answer dear⛄

❥

$\sqrt{ \frac{5}{2} } \: and \: \sqrt{ \frac{ - 5}{2} }$

are the two zeroes of the polynomial

• p(x) = 8x⁴ + 8x³ - 18x² - 20x - 5

➠ (x - $\sqrt{ \frac{5}{2}$ ) (x + $\sqrt{ \frac{5}{2}$

➠ x² - $\frac{ 5 }{ 2 }$

➠ $\frac{ (2x² \: - \: 5) }{ 2 }$

➠ 2x² - 5 is the one of the factor

❥ $\sf\fbox\orange{ Divide \: p(x) \: by \: (2x² - 5) }$

➠ 8x⁴ + 8x³ - 18x² - 20x - 5

➠ (2x² - 5) (4x³ + 4x + 1)

❥ $\sf\fbox\green{ Split \: the \: middle \: terms }$

➠ 4x² + 4x + 1

➠ 4x² + 2x + 2x + 1

➠ 2x(2x + 1) + 1(2x + 1)

➠ (2x + 1) (2x + 1)

• $\large\pink{ x \: = \: \frac{-1}{2}$

❥ $\sf\fbox\blue{ other \: zeroes \: = \: \frac{-1}{2}$

$\huge\colorbox{cyan}{MysticalGiggles}$