Question

Find the quadratic polynomial whose zeros are minus a and minus 1 by a

Answer 1

Answer:

$\sf{Zeroes = } \tt{(-a) , (-\frac{1}{a})}$

Polynomial = x^2 - (sum)x + product

Sum of zeroes = -a - 1/a = (-a^2 - 1)/a

Product of Zeroes = -a ×(-1/a) = 1

Polynomial = x^2 + x(a^2 + 1) +1

__________

Answer 2

Step-by-step explanation:

x² + (-a-1/a)x + (-a)(-1/a) = 0

ax² + (-a²-1)x + a = 0

ax² - a²x - x + a = 0

ax (x-a) - (x-a) = 0

( ax - 1 ) (x-a) = 0