Question

Find all zeros of the polynomial f(x) = 2x⁴ – 2x³ – 7x² + 3x + 6 if its two zeros are (–√3/2) and (√3/2) .

Answer 1

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→ $p(x) = 2{x}^{4} - 2{x}^{3} - 7{x}^{2} + 3x + 6$

Factors of zeros = $( x + \sqrt{\frac{3}{2}})( x - \sqrt{\frac{3}{2}})$

→ ${x}^{2} - \frac{3}{2}$

→ 2x² - 3

By dividing this to the given polynomial we get ,

→ x² - x - 2

→ x² + x - 2x - 2

→ x ( x + 1 ) -2 ( x + 1 )

→ ( x - 2 ) ( x + 1 )

So, it's other zeros are 2 , - 1 .

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