Select the correct answer: Which statement best describes the zeros of the function h(x)=(x-6)(x^2+8x+16)?

Carol Gates

Carol Gates

Answered question

2021-09-05

Select the correct answer: 
Which statement best describes the zeros of the function h(x)=(x6)(x2+8x+16)
1. The function has two distinct real zeros 
2. The function has three distinct real zeros. 
3. The function has one real and two complex zeros. 
4. The function has three complex zeros.

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-09-06Added 99 answers

Step 1 
Given: 
f(x)=(x6)(x2+8x+16) 
Step 2 
Finding its zeroes, which equates the function to zero, gives us, (x6)(x2+8x+16)=0 
The term (x2+8x+16) is a quadratic polynomial which can be factorized by split the middle term method proceeding accordingly, 
(x6)(x2+4x+4x+16)=0 
(x6)[x(x+4)+4(x+4)]=0 
(x6)[(x+4)(x+4)]=0 
Now, if (x6)=0x=6 
if (x+4)=0x=4 
 zeroes of the function are 6 and -4. 
 the function has two distinct real roots , i.e. option (1) is correct.

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