Choose the correct answer from the given four options in the following questions:
The number of polynomials having zeroes as $ -2 $ and 5 is
(A) 1
(B) 2
(C) 3
(D) more than 3

AcademicMathematicsNCERTClass 10

Given: 

Zeroes $-2$ and $5$.

To do: 

We have to find the number of polynomials having zeroes as $-2$ and $5$.

Solution:

Let $\alpha=-2$ and $\beta=5$

Therefore,

$\alpha+\beta=-2+5=3$......(i)

$\alpha\beta=-2\times5=-10$ .......(ii)

This implies,

The polynomial $f( x)=x^2-( \alpha+\beta)x+\alpha\beta$

$\Rightarrow f( x)=x^2-3x-10$

If we multiply $f( x)$ by any constant $k$, roots will be $\alpha$ and $\beta$.

$\Rightarrow P( x)=k( x^2-3x-10)$

Thus, there are infinite number of polynomials possible. 

raja
Updated on 10-Oct-2022 13:27:08

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