Find the Zeros of the Following Quadratic Polynomials x^2-2x-8 And Verify the Relationship Between the Zeros and the Coefficients
By BYJU'S Exam Prep
Updated on: October 17th, 2023
Find the zeros of the following quadratic polynomials x2-2x-8 and verify the relationship between the zeros and the coefficients.
By following these steps, you can find the zeros of a quadratic polynomial and check the relationship between the zeros and the coefficients.
- Set the polynomial equal to zero: ax2 + bx + c = 0.
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Determine whether the polynomial can be factored. If it can be factored, use factoring to find the zeros. If it cannot be factored easily, proceed to step 3.
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Use the quadratic formula to find the zeros if factoring is not possible:
x = (-b ± √(b2 – 4ac)) / (2a)
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Once you have found the zeros, verify the relationship between the zeros and the coefficients using Vieta’s formulas.
Table of content
Find the Zeros of the Following Quadratic Polynomials x2-2x-8 And Verify the Relationship Between the Zeros and the Coefficients
Solution:
To find the zeros of the quadratic polynomial x2 – 2x – 8, we need to solve the equation x2 – 2x – 8 = 0. We can do this by factoring or by using the quadratic formula.
Factoring: x2 – 2x – 8 = 0 (x – 4)(x + 2) = 0
Setting each factor equal to zero: x – 4 = 0 => x = 4 x + 2 = 0 => x = -2
So the zeros of the quadratic polynomial x2 – 2x – 8 are x = 4 and x = -2.
Now let’s verify the relationship between the zeros and the coefficients. For a quadratic polynomial of the form ax2 + bx + c = 0, the relationship between the zeros and the coefficients can be expressed using Vieta’s formulas.
In this case, the quadratic polynomial is x2 – 2x – 8 = 0.
According to Vieta’s formulas, the sum of the zeros is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. In other words:
Sum of zeros = -b/a
The product of the zeros is equal to the constant term divided by the coefficient of the quadratic term. In other words:
Product of zeros = c/a
For our polynomial x2 – 2x – 8 = 0:
Sum of zeros = -(-2)/1 = 2/1 = 2 Product of zeros = -8/1 = -8
Indeed, the sum of the zeros, 4 and -2, is 2, and the product of the zeros is -8, which matches the relationship given by Vieta’s formulas.
Answer:
Zeros of the Following Quadratic Polynomials x2-2x-8 are 4 and -2. And the Relationship between the Zeros and the Coefficients is Verified
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