Find the zeros of the following quadratic polynomials x^2-2x-8 and verify the relationship between the zeros and the coefficients.

Jaquan Ramsey

Jaquan Ramsey

Answered question

2023-03-22

Find the zeros of the following quadratic polynomials x2-2x-8 and verify the relationship between the zeros and the coefficients.

Answer & Explanation

chumanhonv19s

chumanhonv19s

Beginner2023-03-23Added 4 answers

Step 1: Form the equation
The given polynomial is x2-2x-8.
We are aware that a polynomial's zeroes are evaluated by equating them to zero.
px=0
x2-2x-8=0
Step 2: Solve to find the zeroes
x2-2x-8=0
x2-4x+2x-8=0
xx-4+2x-4=0
x-4x+2=0
x=4,-2
Step 3: Verification
For a specific polynomial, we are aware that ax2+bx+c,
Sum of the zeroes=-ba and product of the roots=ca
Sum of the zeroes =4-2=2
Again, -ba=--21=2
Product of the zeroes =4-2=-8
Again, ca=81=8
As a result, the polynomial's zeroes and coefficients are proven to be related.
Therefore, the zeroes of this polynomial are 4 and -2.

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