Question

If a quadratic polynomial f (x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?

Answer 1

The total number of real and distinct zeros of f(x) is two

Step-by-step explanation:

Given that a quadratic polynomial f(x) is factorizable into linear distinct factors

To find the total number of real and distinct zeros of f(x) :

• Let f(x)=ax^2+bx+c=0[/tex]
• Since the quadratic polynomial f(x) is factorizable into linear distinct factors.
• If we put the value of it must satisfy the given polynomial hence it must be a zero

• That is f(x)=0

• A quadratic equation with real coefficients can have either one or two distinct real roots.  Since there are 2 distinct roots we that the discriminant is positive

• Since the given polynomial is quadratic its degree is 2
• Hence the number of zeros can be calculated with the degree of the polynomial.
• Therefore the polynomial f(x) must have two zeros

Therefore  the total number of real and distinct zeros of f(x) is two