Question

if p( x) =ax2+bx +c is a quadratic polynomial then what is relation of c/a with zeros of p (x)?​

Answer 1

ax² + bx + c

Let the zeroes of p (x) be α and β

Product of zeores = c/a

αβ = c/a

Answer 2

Answer:

If $p(x) = ax^2+bx+c$ is a quadratic polynomial then the relation of c/a with zeroes of $p(x)$ is like the product of zeroes is equal to c/a.

Step-by-step explanation:

We have a quadratic polynomial as $p(x) = ax^2+bx+c$ and it is asked to give a relation between zeroes of polynomial and c/a

Let the zeroes of polynomial be α and β so that our calculation becomes easier.

Then there is a common rule which says that

• Sum of zeroes = α + β = -(Coeffiecient of x)/Coefficient of x²

⇒α + β = (-b)/a

• Prodct of Zeroes = α.β = Constant term/ Coefficient of x²

⇒α×β = c/a

So from here, it is clear that the actual relation between c/a and zeroes of a polynomial is like the product of zeroes of a polynomial is directly equal to c/a