Question

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

Answer 1

$\large{\bold{ \underline{ \underline{ \: \: Given \: \: \: \: }}}}$

$\bold{Sum \: of \: the \: zeroes \: (α )= \frac{3}{2} }$

$\bold{Product \: of \: the \: zeroes \: ( β ) = \frac{ - 2}{5} }$

$\large{\bold{ \underline{ \underline{ \: \: \:Answer \: \: \: }}}}$

$\to \bold{ 10 {x}^{2} - 11x - 6} \: = 0$

$\large{\bold{ \underline{ \underline{ \: \: Explanation \: \: \: }}}}$

$\bold{ \underline{We \: know \: that , \: \: \: }}$

$\large\fbox{ \fbox{\bold{Quadratic \: polynomial = x - ( \bold{ α + β }) x + αβ \: = 0}}}$

$\to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{3}{2} + ( - \frac{2}{5} )) + ( \frac{3}{2}( \frac{ - 2}{5} ) ) = 0} \\ \\ \to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{3}{2} - \frac{2}{5} ) - \frac{6}{10} = 0 } \\ \\ \to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{15 - 4}{10} )x - \frac{6}{10} = 0} \\ \\ \to \bold{Required \: quadratic \: polynomial = 10 {x}^{2} - 11x - 6 = 0}$

Therefore , 10x² - 11x - 6 = 0 is the required quadratic polynomial

Answer 2

Step-by-step explanation:

\large{\bold{ \underline{ \underline{ \: \: Given \: \: \: \: }}}}

Given

\bold{Sum \: of \: the \: zeroes \: (α )= \frac{3}{2} }Sumofthezeroes(α)=

2

3

\bold{Product \: of \: the \: zeroes \: ( β ) = \frac{ - 2}{5} }Productofthezeroes(β)=

5

−2

\large{\bold{ \underline{ \underline{ \: \: \:Answer \: \: \: }}}}

Answer

\begin{gathered}\to \bold{ 10 {x}^{2} - 11x - 6} \: = 0 \\\end{gathered}

→10x

2

−11x−6=0

\large{\bold{ \underline{ \underline{ \: \: Explanation \: \: \: }}}}

Explanation

\bold{ \underline{We \: know \: that , \: \: \: }}

Weknowthat,

\begin{gathered}\large\fbox{ \fbox{\bold{Quadratic \: polynomial = x - ( \bold{ α + β }) x + αβ \: = 0}}} \\\end{gathered}

\begin{gathered}\to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{3}{2} + ( - \frac{2}{5} )) + ( \frac{3}{2}( \frac{ - 2}{5} ) ) = 0} \\ \\ \to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{3}{2} - \frac{2}{5} ) - \frac{6}{10} = 0 } \\ \\ \to \bold{Required \: quadratic \: polynomial = {x}^{2} - ( \frac{15 - 4}{10} )x - \frac{6}{10} = 0} \\ \\ \to \bold{Required \: quadratic \: polynomial = 10 {x}^{2} - 11x - 6 = 0} \\\end{gathered}

→Requiredquadraticpolynomial=x

2

−(

2

3

+(−

5

2

))+(

2

3

(

5

−2

))=0

→Requiredquadraticpolynomial=x

2

−(

2

3

−

5

2

)−

10

6

=0

→Requiredquadraticpolynomial=x

2

−(

10

15−4

)x−

10

6

=0

→Requiredquadraticpolynomial=10x

2

−11x−6=0

Therefore , 10x² - 11x - 6 = 0 is the required quadratic polynomial