Home
Class 10
MATHS
If a is a zero of f(x) then, is one of ...

If a is a zero of f(x) then, _____ is one of the factors of f(x).

A

(x-2a)

B

(x-a)

C

(x+a)

D

(2x-a)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to understand the relationship between the zeros of a polynomial and its factors, specifically using the Factor Theorem. ### Step-by-Step Solution: 1. **Understanding the Problem**: The question states that if 'a' is a zero of the polynomial function f(x), we need to identify what can be concluded about the factors of f(x). 2. **Applying the Factor Theorem**: According to the Factor Theorem, if 'a' is a zero of the polynomial f(x), it means that when we substitute 'a' into the polynomial, f(a) = 0. 3. **Identifying the Factor**: The Factor Theorem also states that if f(a) = 0, then (x - a) is a factor of the polynomial f(x). This means that the polynomial can be expressed as f(x) = (x - a) * g(x), where g(x) is another polynomial. 4. **Conclusion**: Therefore, if 'a' is a zero of f(x), then (x - a) is one of the factors of f(x). ### Final Answer: If 'a' is a zero of f(x), then **(x - a)** is one of the factors of f(x). ---
Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 3

    OSWAL PUBLICATION|Exercise Section -A|6 Videos

  • SAMPLE PAPER 3

    OSWAL PUBLICATION|Exercise Section B|2 Videos

  • SAMPLE PAPER 2

    OSWAL PUBLICATION|Exercise QUESTION BANK|99 Videos

  • SAMPLE PAPER 4

    OSWAL PUBLICATION|Exercise Section -C|8 Videos

Similar Questions

Explore conceptually related problems

If f(x+3)=x^(2)+x-6 , then one of the factors of f(x) is ________.

If f(x+1)=2x^(2)+7x+5 , then one of the factors of f (x) is ______.

If f(x)=x^(2)-2x-3 , then find the zeroes of f(x).

if f (x) satisfies condition in Rolle's theorem then show that between two consecutive zeros of f(x) there lies at most one zero of f(x).

If (x-1) is a factor of polynomial f(x) but not of g(x) ,then it must be a factor of f(x)g(x)(b)-f(x)+g(x)f(x)-g(x)(d){f(x)+g(x)}g(x)

If a,b,c are real roots of the cubic equation f(x)=0 such that (x-1)^(2) is a factor of f(x)+2 and (x+1)^(2) is a factor of f(x)-2, then abs(ab+bc+ca) is equal to

If f(x) and g(x) are two polynomials with integers coefficient which vanish at x = 1 / 2, then what is the factor of HCF of f(x) and g(x) ?

If f(x)=0 is a R.E.of first type and odd degree then a factor of f(x) is

All zeroes of f(x) =x^(2)-2x are _____.

f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If f'(x) ne 0 , then maximum number of real roots of f''(x) = 0 is /are