Question

If √2 is the zero of polynomial find all the zeroes of 6x^3+√2x^2-10-√4x^2

Answer 1

Answer:

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Answer 2

Here is your answer dear⛄

❥ Given :-

▶ √2 is the one of the zero of the cubic polynomial

▶Then (x - √2) is one of the factor of the given polynomial

• p(x) = 6x³ + √2x² - 10x - 4√2

☞ $\large\fbox\pink{ Divide \: p(x) \: by \: (x - √2) }$

• 6x³ + √2x² - 10x - 4√2
• (x - √2) (6x² + 7√2x + 4)
• (x - √2) (6x² + 4√2x + 3√2x + 4)

☞ $\large\fbox\green{ Split \: the \: middle \: term }$

• (x - √2) [ 2x(3x + 2√2) + √2(3x + 2√2) ]
• (x - √2) (2x + √2) (3x + 2√2)

☞ $\large\fbox\red{ Put \: p(x) \: = \: 0 }$

• (x - √2) (2x + √2) (3x + 2√2) = 0

✑ x = √2 , x = $\frac{ -√2}{2}$ , x = $\frac{-2√2}{3}$

✑ x = √2 , x = $\frac{-1}{√2}$ , x = $\frac{-2√2}{3}$

☞ $\large\fbox\purple{ Rationalising \: Second \: Zero }$

$\huge\blue{ Hence }$ , the other two zeroes of p(x) are $\frac{ -1 }{ √2 }$ & $\frac{ -2√2 }{ 3 }$

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