Question

Find the quadratic polynomial whose sum and product of zeroes are √2 −1 and 1
√2−1

Answer 1

$\huge\bf\purple{\mid{\fbox{\underline{\underline{\maltese{Answer}\maltese}}}}\mid}$

x² + 2x - 3

a = 1 , b = 2 and c = -3

=> x = $\frac{-b ± \sqrt { b² - 4ac}}{2a}$

=> x = $\frac{–2 ± \sqrt { (2)² - 4×1×(-3)}}{2×1}$

=> x = $\frac{–2 ± \sqrt { 4 + 12}}{2}$

=> x = $\frac{–2 ± \sqrt {16}}{2}$

=> x = $\frac{–2 ± 4}{2}$

=> x = $\frac{–2 + 4}{2}$ , $\frac{–2 – 4}{2}$

=> x = $\frac{2}{2}$ , $\frac{–6}{2}$

=> x = 1 , -3

Hence zeroes of the polynomials are -3 and 1 .

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