Question

Find the quadratic polynomial the sum and product of whose zeroes are 2 and - 3 / 5

Answer 1

Hello dear user ...

Solution ↓
$given \: \\ \\ sum \: \: of \: zeros( \alpha + \beta ) = 2 \\ \\ and \: \\ \\ product \: of zeros \: = \alpha \beta = \frac{ - 3}{5}$
Hence , required Polynomial =

${x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = > {x}^{2} - 2x + ( \frac{ - 3}{5} ) \\ \\ = > 5 {x}^{2} - 10x - 3$
so the quadratic Polynomial is

5x^2 - 10x - 3

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Hope it's helps you
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Answer 2

Hey!

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•Sum of zeroes

=> α + β = - b ÷ a = -(Coefficient of x) ÷ (Coefficient of x²)

•Product of Zero

=>α × β = c ÷ a = (Constant term ÷ Coefficient of x²)

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Given :-

•Sum of zero

=> (α + β) = 2

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•Product of zeroes :-

=> (α × β) = -3 ÷ 5

Now :-

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•Writing the polynomial in term of sum of zeroes and product of zeroes :-

P(x) = ax² + bx + c = 0

= a[ x² + b ÷ a × x + c ÷ a]

= a[ x² - (- b ÷ a) × x + c ÷ a]

= a[x² - (sum of zeroes)x + (Product of zeroes)]

= a[x² - (α + β)x + αβ]

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= x² - 2x + (-3 ÷ 5)

= 5x² - 10x - 3

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Regards

Cybary

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