Question

Find a quadratic polynomial,thesum and product of whose zeroes are√3and1/√3respectively.​

Answer 1

HERE IS YOUR ANSWER...

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$sum \: of \: zeroes = \sqrt{3} \\ product \: of \: zeroes = \frac{1}{ \sqrt{3} } \\ \alpha + \beta = \frac{ - b}{a} \\ \sqrt{3} + \frac{1}{ \sqrt{3} } = \frac{ - b}{a} \\ \frac{3 + 1}{ \sqrt{3} } = \frac{ - b}{a} \\ \frac{4}{ \sqrt{3} } = \frac{ - b}{a} \: \: \: \: ... \: \: ... \: \: ...eq(1) \\ \alpha \beta = \frac{c}{a} \\ \sqrt{3} \times \frac{1}{ \sqrt{3} } = \frac{c}{a} \\ 1 = \frac{c}{a} ... \: \: ... \: \: ... \: \: eq(2) \\ from \: eq(1) \: and \: eq(2) \: we \: get... \\ a = \sqrt{3} \\ b = - 4 \\ c = 1 \\ quadratic \: equation \: = a {x}^{2} + bx + c \\ \sqrt{3} { x}^{2} + ( - 4)x + 1 \\ > > > > > > \sqrt{3} {x}^{2} - 4x + 1 < < < < < <$

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