Question

find the quadratic polynomial for the zeroes 1/2?3/2​

Answer 1

Answer:

Given zeroes :-

1 / 3 and -2

Let

\begin{gathered} \alpha = \frac{1}{3 } \\ \end{gathered}

α=

3

1

And

\beta = - 2β=−2

Now,

Sum of the zeroes :-

\begin{gathered} = \alpha + \beta \\ \\ \\ = \frac{1}{3} + ( - 2) \\ \\ \\ = \frac{1 - 6}{3} \\ \\ \\ = \frac{ - 5}{3} \end{gathered}

=α+β

=

3

1

+(−2)

=

3

1−6

=

3

−5

Product of zeroes :-

\begin{gathered} = \alpha \beta \\ \\ \\ = \frac{1}{3} \times - 2 \\ \\ \\ = \frac{ - 2}{3} \end{gathered}

=αβ

=

3

1

×−2

=

3

−2

Now,

Required polynomial is :-

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

\begin{gathered}p(x) = {x}^{2} - ( \frac{ - 5}{3} ) + ( \frac{ - 2}{3} ) \\ \\ \\ p(x) = {x}^{2} + \frac{5}{3} - \frac{2}{3} \end{gathered}

p(x)=x

2

−(

3

−5

)+(

3

−2

)

p(x)=x

2

+

3

5

−

3

2

Answer 2

Step-by-step explanation:

if the given zeroes are 1/2 and 3/2

thats means

α=1/2. and β=3/2

therefore required quadratic polynomial is.

f(x)= x^2 -(α+β)x + αβ

f(x)= x^2 -(1/2+3/2)x +1/2.3/2

f(x)= x^2- (4/2)x +3/4

f(x)= x^2 - 2x +3/4 Ans.