Home
Class 12
MATHS
If -7 and 5 are both zeros of the polyno...

If `-7 and 5` are both zeros of the polynomial q(x), then a factor of q(x) is

A

`x^(2)-35`

B

`x^(2)+35`

C

`x^(2)+2x+35`

D

`x^(2)+2x-35`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find a factor of the polynomial \( q(x) \) given that the zeros of the polynomial are \( -7 \) and \( 5 \). ### Step-by-Step Solution: 1. **Understanding Zeros of a Polynomial**: If \( -7 \) and \( 5 \) are zeros of the polynomial \( q(x) \), it means that \( q(-7) = 0 \) and \( q(5) = 0 \). This implies that \( (x + 7) \) and \( (x - 5) \) are factors of \( q(x) \). 2. **Writing the Factors**: Since the zeros are \( -7 \) and \( 5 \), we can express the polynomial \( q(x) \) in terms of its factors: \[ q(x) = (x + 7)(x - 5) \] 3. **Expanding the Factors**: Now, we will expand \( (x + 7)(x - 5) \): \[ q(x) = x^2 - 5x + 7x - 35 \] Combine like terms: \[ q(x) = x^2 + 2x - 35 \] 4. **Identifying a Factor**: From the expression \( q(x) = (x + 7)(x - 5) \), we can see that one of the factors of \( q(x) \) is \( (x + 7) \) or \( (x - 5) \). ### Final Answer: Thus, a factor of \( q(x) \) is \( (x + 7) \) or \( (x - 5) \). ---
Promotional Banner

Similar Questions

Explore conceptually related problems

If 5 and -1 are both zeros of the polymonial P(x), then a factor of P(x) is

Zero of the polynomial p(x) =2x+5 is

Write the zeros of the polynomial x^2-x-6 .

x+1 is a factor of the polynomial

If alpha and beta are the zeros of the polynomial f(x)=x^2+p x+q , then a polynomial having 1/alpha and 1/beta as its zeros is ........................................................... (a) x^2+q x+p (b) x^2-p x+q (c) q x^2+p x+1 (d) p x^2+q x+1

One of the zeroes of the polynomial 2x^(2)+7x-4 is

If 1 and -1 are zeroes of the polynomial x^(3)+5x^(2)-x-5 , then find all zeroes of the given polynomial.

If alpha and beta are the zeros of the polynomial f(x)=x^2+p x+q , form a polynomial whose zeros are (alpha+beta)^2 and (alpha-beta)^2 .

Find zeroes of the polynomial 5x^(2)-4-8x .