If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

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What’s inside this PDF?

Question: If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

Options:

-8
-4
4
8

Correct Answer: -4

Solution:

If one root is 2, then the other root can be found using the product of the roots: 2 * r = 6, so r = 3. The sum of the roots is 2 + 3 = -p, thus p = -5.

If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

Practice Questions

If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

-8
-4
4
8

Questions & Step-by-Step Solutions

If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

Step 1: Start with the equation x^2 + px + 6 = 0.
Step 2: We know one root of the equation is 2.
Step 3: Use the fact that the product of the roots (2 * r) equals the constant term (6).
Step 4: Set up the equation: 2 * r = 6.
Step 5: Solve for r by dividing both sides by 2: r = 6 / 2 = 3.
Step 6: Now we have both roots: 2 and 3.
Step 7: The sum of the roots is 2 + 3 = 5.
Step 8: According to Vieta's formulas, the sum of the roots is also equal to -p.
Step 9: Set up the equation: 5 = -p.
Step 10: Solve for p by multiplying both sides by -1: p = -5.

Quadratic Equations – Understanding the properties of roots, including the sum and product of roots in a quadratic equation.
Vieta's Formulas – Applying Vieta's formulas to relate the coefficients of a polynomial to sums and products of its roots.

If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

What’s inside this PDF?

If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

Practice Questions

Questions & Step-by-Step Solutions

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