Question

find the quadratic polynomial whose zeroes are √2 and 1/3
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Answer 1

SOLUTION:-

Let the zeros of quadratic polynomial be α and β.

•°• α = √(2) and β = 1/3

now,

$</p><p>\tt \: \alpha + \beta \: = \frac{3 \sqrt{2}+1}{3} \\ \\ </p><p>\tt \: And, \: \: \\ \\ </p><p>\tt \: \alpha \beta \: = \: \frac{\sqrt{2}}{3} \\ \\ \\ </p><p></p><p>\texttt {\red { The required Quadratic polynomial = }} \\ \\ </p><p></p><p>\tt \orange {\: = \: x^2 - (\alpha + \beta)x + \alpha \beta} \\ \\ </p><p></p><p>\tt \therefore = x^2 - \frac{3 \sqrt{2}+1}{3} \times x + \frac{\sqrt{2}}{3} \\ \\ </p><p></p><p>\tt \: \: x^2 - (\frac{3 \sqrt{2}+1}{3})x + \frac{\sqrt{2}}{3} \: = \: 0 \\ \\ \tt \: is \: Answer. </p><p></p><p>$