Question

Form a quadratic polynomial, one of whose zero is √5 and the product of its zeroes is -2√5.

Answer 1

Given:

product of the zeroes ✔-2√5

and the other zeroes ✔√5

To find:

Polynomial

$\huge{\mathcal{\blue{Answer}}}$

First we have to find the other zeroes

let x and y are the zeroes of the polynomial

we have

$x \times y = - 2 \sqrt{5} \\ x \times \sqrt{5} = - 2 \sqrt{5} \\ x = - 2$

now we have the two zeores:

$x = - 2...........x = \sqrt{5} \\ x + 2 = 0....(1)......x - \sqrt{5} = 0....(2)$

Multiplying (1) and (2) we get

$(x + 2)(x - \sqrt{5} ) = 0 \\ x {}^{2} - x \sqrt{5} + 2x - 2 \sqrt{5} = 0 \\ x {}^{2} - x( \sqrt{5} - 2) - 2 \sqrt{5} = 0$

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Answer 2

${\huge{\boxed{\bold{\red{\boxed{Happy\: Diwali}}}}}}$

$\huge\underline\mathfrak\purple{Answer}$

°•° Let

$\alpha \times \beta = - 2 \sqrt{5} . \\ \\ \sqrt{5} \times \beta = - 2 \sqrt{5} . \\ \\ \beta = \cancel \frac{ - 2 \sqrt{5} }{ \sqrt{5} } \\ \\ \beta = - 2.$

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