How Can You Verify the Sum of Roots in a Quadratic Equation?

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In summary, we can verify the statement A + B = -b/a by adding the two solutions of the quadratic equation and simplifying the resulting expression. This is due to the fact that the radicals in the solutions cancel out, leaving us with -b/a.
  • #1
mathdad
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Let A and B be roots of the quadratic equation
ax^2 + bx + c = 0. Verify the statement.

A + B = -b/a

What are the steps to verify this statement?
 
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  • #2
RTCNTC said:
Let A and B be roots of the quadratic equation
ax^2 + bx + c = 0. Verify the statement.

A + B = -b/a

What are the steps to verify this statement?
There is a theorem for this, but let's do it logically. The two solutions, A and B of the quadratic are
\(\displaystyle A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\) and \(\displaystyle B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Now add the two. (Hint: What happens to the radicals?)

-Dan
 
  • #3
topsquark said:
There is a theorem for this, but let's do it logically. The two solutions, A and B of the quadratic are
\(\displaystyle A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\) and \(\displaystyle B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Now add the two. (Hint: What happens to the radicals?)

-Dan

The radicals disappear. We are then left with (-2b)/(2a).
Of course, (-2b)/(2a) simplifies to -b/a.
 

FAQ: How Can You Verify the Sum of Roots in a Quadratic Equation?

What is the purpose of verifying a statement in scientific research?

The purpose of verifying a statement in scientific research is to ensure that the information presented is accurate and supported by evidence. This helps to maintain the credibility and reliability of scientific findings.

How do scientists verify a statement?

Scientists verify a statement by conducting experiments, collecting data, and analyzing results. They also review previous research and consult with other experts in the field to ensure the validity of their statement.

What is the difference between verifying a statement and proving a statement?

Verifying a statement involves providing evidence and supporting data to support the statement, while proving a statement requires absolute certainty and no room for doubt. In scientific research, statements are often verified rather than proven.

Can a statement be verified if it goes against existing theories or beliefs?

Yes, a statement can still be verified if it goes against existing theories or beliefs. In fact, this is often the case in scientific research as new findings may challenge previous beliefs and lead to a shift in understanding.

Why is it important to replicate experiments when verifying a statement?

Replicating experiments is important in verifying a statement because it allows for the confirmation of results and ensures that the findings are not due to chance. It also helps to identify any potential errors or biases in the original experiment.

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