Question

★Question-:


Find the quadratic polynomial sum and product of whose zeroes are $-1$ and $-20$ respectively. Also, find the zeroes of the polynomial so obtained.

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Answer 1

$\huge \underline{QᴜᴇSᴛɪᴏɴ :-}$

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Find the quadratic polynomial sum and product of whose zeroes are -1 and -20 respectively. Also, find the zeroes of the polynomial so obtained.

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$\huge \underline{ᴀɴSᴡᴇʀ:-}$

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• Zeroes of polynomial are -5 and 4

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$\huge\underline{ᴡʜᴀᴛ \: ᴛᴏ \: ᴅᴏ :-}$

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We know that, polynomial is in the form of x² - (sum of roots) x + product of roots. Then the we will find the roots of obtained polynomial by factorising it.

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$\huge \underline{ɢɪᴠᴇɴ:-}$

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• sum of roots = -1
• product of roots = -20

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$\huge \underline{Sᴏʟᴜᴛɪᴏɴ :-}$

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$\bf x² - (sum \: of \: roots) x + product \: of \: roots$

$\bf: \implies {x}^{2} - ( - 1x) + ( - 20)$

$\bf: \implies {x}^{2} + x - 20$

Now we have to factorize it

$\bf: \implies {x}^{2} + x - 20$

$\bf: \implies {x}^{2} + 5x - 4x - 20$

$\bf: \implies x(x + 5) - 4(x + 5)$

$\bf: \implies (x + 5)(x - 4)$

Let the zeroes be alpha and beta. So,

$\bf\to \alpha = x + 5 = 0$

$\bf\to \alpha = x = - 5$

$\bf\to \beta = x - 4 = 0$

$\bf\to \beta = x = 4$

Therefore, Zeroes of polynomial are -5 and 4.

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$\bf \purple{thank \: you} \pink\hearts$

Answer 2

Step-by-step explanation:

Given :

• Sum of zeroes = -1
• Product of zeroes = -20

To find :

• Quadratic polynomial.
• Zeroes of the polynomial.

Solution :

We know:

General quadratic equation form :-

=> x² - (Sum of zeroes)x + (Product of zeroes)

=> x² - (-1)x + (-20)

=> x² + x - 20

Factorizing by splitting the middle term :-

=> x² + x - 20

=> x² + 5x - 4x - 20

=> x(x + 5) - 4(x + 5)

=> (x - 4)(x + 5) = 0

∴ x = 4 or x = -5

∴ The zeroes of the polynomial are 4 and -5.