Question

Find a quadratic polynomial, the sum and product of zeroes are -3 and 2 respectively.​

Answer 1

$\huge \boxed{ \red{ \mathfrak{solution}}}$

Given:

◆ Sum of zeroes = -3

and

◆ product of zeroes= 2

As we know :

Quadratic polynomial =

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

put the values , we get

$\leadsto \: {x}^{2} - ( -3)x + 2 \\ \\ \leadsto \: {x}^{2} + 3x + 2$

Hence the required polynomial is

$\huge \boxed{ \purple{{x}^{2} + 3x + 2}}$

Answer 2

$\huge\star{\underline{\tt{\red{Answer}}}}\star$

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Given:

Sum of zeroes = -3

Product of zeroes = 2

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Formulae

• Sum of zeroes = $\dfrac{-b}{a} = \alpha + \beta$
• Product of zeroes = $\dfrac{c}{a} = \alpha \times \beta$

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SoluTion:

Let the Quadratic Equation be ax²+bx+c =0

So,

We know by the formula

$\implies Sum\:of\:zeroes = \dfrac{-3}{1} = \dfrac{-b}{a} \\ \implies Here, \\ -b=-3 \implies \boxed{b=3} \\ \implies Product\:of\:zeroes = \dfrac{2}{1} = \dfrac{c}{a} \\ \implies Here, \\ \boxed{c= 2} \\ Also,\boxed{a=1}$

Quadratic Equation will be

$(1)x^2 +(3)x + (2) \\ \\ \huge{\boxed{x^2 + 3x+2}}$