Question

a polynomial is given as p(x) = ax 2 + 82x + a.
If −9 is one of the zeroes of the polynomial, then what is its other zero?

Answer 1

Answer:

$\text{Given Equation:}$

$ax^2 + 82x + a = 0\\\\\text{where } f(-9) = 0\\\\f(-9) = a(-9)^2 + 82(-9) + a = 0\\\\81a - 738 + a = 0\\\\82a = 738\\\\\text{\boxed{a = 9}}\\\\\text{Hence, equation is: }\\\\9x^2 + 82x + 9 = 0\\\\9x^2 + 81x + x + 9 = 0\\\\9x(x + 9) + 1(x + 9) = 0\\\\(x + 9)\text{ }(9x + 1) = 0 \\\\x = -9 \text{ or } x = -\frac{1}{9} \\\\\boxed{\text{Answer = -1/9 is the other root.}}\\ \\\text{If you liked the answer please feel free to mark it brainliest.}$

Answer 2

Answer:

in such questions, simply write the reciprocals of the root that is given. so, the answer in this case is -1/9

Step-by-step explanation: