Question

find the quadratic polynomial whose sum and product of the zeros are a and 1/a

Answer 1

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Here is your answer
Sum of zeros is a

Product of zeros is 1/a

As we know that quadratic polynomial is
$x {}^{2} - (sum \: of \: zeros)x + (product \: of \: zeros) = 0\\ x {}^{2} - ax + \frac{1}{a} = 0 \\ ax {}^{2} - a {}^{2}x + 1 = 0$

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Answer 2

Answer:

$\text{The quadratic polynomial is }ax^2-a^2x+1$

Step-by-step explanation:

Given the sum and product of zeroes of quadratic polynomial

we have to find the quadratic polynomial.

$\text{sum of zeroes=}a$

$\text{product of zeroes=}\frac{1}{a}$

The quadratic polynomial is

$x^2-(\text{sum of zeroes})x+(\text{product of zeroes})$

Multiplying by a on both sides

$x^2-ax+\frac{1}{a}$

$ax^2-a^2x+1$

which is required quadratic polynomial.