Solution:
Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x) = ax2 + bx + c$ where a, b, c, ∈ R and a ≠ 0.
Given,
John and Jilani together have a total of $45 $marbles.
Let John have$ x$ marbles.
So, Jivani will be having $(45 – x) $marbles.
Number of marbles John had after losing $5 $marbles =$ x – 5$
Number of marbles Jivani had after losing $5$ marbles = $(45 – x) – 5 = 40 – x$
Now, according to the question the product of the marbles that they are having now is 128
So,
$(x – 5)(40 – x) = 128$
⇒$ 40x – x2 – 200 = 128$
⇒ $x2 – 45x + 128 + 200 = 0$
⇒$ x2 – 45x + 328 = 0$
Thus the required quadratic equation is $x2 – 45x + 328 = 0$.