Question

find the quadratic polynomial whose zeros are - 9 and 1 upon - 9 ​

Answer 1

Let,

alpha = -9

and

Beta = -1/9

P(x) = x² -(alpha+beta)x + alpha.beta

P(x) = x²-[-9+(-1/9)]x + -9×-1/9

P(x) = x²-[-81-1/9]x +1

P(x) = x² + 82/9x + 1

Answer 2

The required polynomial is $P=x^2+(\frac{82}{9})x+1$.

Step-by-step explanation:

Given : The zeros are -9 and $\frac{1}{-9}$.

To find : The quadratic polynomial ?

Solution :

The zeros of the quadratic polynomial is $\alpha=-9,\beta=-\frac{1}{9}$

The quadratic polynomial is given by,

$P=k(x^2-(\alpha+\beta)x+\alpha\beta)$

Substitute the values,

$P=k(x^2-(-9+\frac{1}{-9})x+(-9)(\frac{1}{-9}))$

$P=k(x^2-(\frac{-81-1}{9})x+1)$

$P=k(x^2+(\frac{82}{9})x+1)$

When k = 1,

$P=x^2+(\frac{82}{9})x+1$

#Learn more

Find the quadratic polynomial whose sum and product of zeroes are 9 and 1/9

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