Question

Find a quadratic polynomial whose zeroes are -2/√3 and √3 /4

Answer 1

Answer:

Let α = - 2/√3 and β = √3/4,

$\alpha + \beta = \frac{ - 2}{ \sqrt{3} } + \frac{ \sqrt{3} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 8 + 3}{4 \sqrt{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 5}{4 \sqrt{3} } \\ \\ \alpha \beta = \frac{ - 2}{ \sqrt{3} } \times \frac{ \sqrt{3} }{4} \\ \\ \alpha \beta = \frac{ - 1}{2}$

We know that ;

Quadratic polynomial is given by ;

x² + ( α + β )x - αβ

⇒ x² ( - 5 / 4√3)x - (-1/2)

⇒ x² - 5/4 √3x + 1/2

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