Question

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Chapter-Quadratic Polynomial

Find a quadratic polynomial whose sum of zeros is 9 / 2 and product of zeros is 2 ​

Answer 1

$\LARGE\underline{\underline{\textsf{\textbf{Given\::-}}}}$

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• Sum of zeroes of quadratic polynomial (S) = 9/2

• Product of zeroes of a quadratic polynomial (P) = 2

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$\LARGE\underline{\underline{\textsf{\textbf{To\:Find\::-}}}}$

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• Quadratic polynomial ?

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$\LARGE\underline{\underline{\textsf{\textbf{Solution\::-}}}}$

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• We clearly know that, for finding a quadratic polynomial with sum of zeroes = S, and product of zeroes = P, we use equation ::

• $\Large\boxed{\bf{p(x) = x^2 - Sx + P}}$

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$\underline{\sf{\bigstar\:Putting\:all\:known\:values\:::}}$

$\\ \quad \longrightarrow \quad \sf p(x) = x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2$

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$\underline{\sf{\bigstar\:Multiplying\:the\:equation\:with\:2\:::}}$

$\\ \quad \longrightarrow \quad \sf p(x) = 2\Bigg(x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2\Bigg)$

$\\ \quad \longrightarrow \quad \sf p(x) = \big(2\:\times\:x^2\big) - \bigg(\dfrac{9}{\cancel{2}}\:\times\:\cancel{2}\bigg)x + \big(2\:\times\:2\big)$

$\\ \quad \longrightarrow \quad \large \bf p(x) = 2x^2 - 9x + 4$

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$\therefore\:{\underline{\sf{Hence,\:required\:polynomial\:is\:\bf{2x^2 - 9x + 4}}}}$

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$\LARGE\underline{\underline{\textsf{\textbf{Explore\:More\::-}}}}$

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• If α and β are zeroes of the quadratic polynomial ax² + bx + c, then α + β = -b/a and αβ = c/a.

• If α, β, γ are the zeroes of cubic polynomial ax³ + bx² + cx + d, then α + β + γ = -b/a, αβ + βγ + γα = c/a and αβγ = -d/a.

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$\LARGE\underline{\underline{\textsf{\textbf{Learn\:more\:on\:brainly\::-}}}}$

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$\underline{\sf{\bigstar\:Question\:::}}$

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Find zeroes of the quadratic polynomial 4x² - x - 5 and verify relationship between it's zeroes and coefficients.

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$\underline{\sf{\bigstar\:Answer\:::}}$

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https://brainly.in/question/42964609

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Answer 2

Answer:

Given,

Sum of zeroes of any polynomial is = 9/2

Product of zeroes of any polynomial is = 2

To find :

A quadratic polynomial

Method :

General formula of quadratic polynomial :

$\bf {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes$

Here

$\odot \: \sf \: sum \: of \: zeroes \: can \: be \: represented \: by \: \\ ( \alpha + \beta ) \\ \\ and \\ \\ \odot\sf \: product \: of \: zeroes \: can \: be \: represented \: by \\ \: \alpha \beta$

So quadratic polynomial is :

$\bf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

So according to the question, we can write that,

$\alpha + \beta = \frac{9}{2} \: \: \: \: and \\ \alpha \beta = 2$

So the quadratic polynomial is :

$\bf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = \bf \: {x}^{2} - \frac{9}{2} x + 2$

To learn more :

If α and β are zeroes of the quadratic polynomial ax² + bx + c, then

$\alpha + \beta = - \: \frac{b}{a} \\ \\ \alpha \beta = \frac{c}{a}$