If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the foll

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Question: If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?

Options:

Correct Answer: p + q = -b/a and pq = c/a

Solution:

According to Vieta\'s formulas, the sum of the roots p and q is -b/a and the product is c/a.

If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?

If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?

Step 1: Understand that a quadratic equation is in the form ax^2 + bx + c = 0.
Step 2: Identify the coefficients a, b, and c in the equation.
Step 3: Recognize that the roots of the equation are the values of x that make the equation equal to zero.
Step 4: Learn about Vieta's formulas, which relate the coefficients of the polynomial to the sums and products of its roots.
Step 5: According to Vieta's formulas, the sum of the roots p and q is given by the formula -b/a.
Step 6: Also, according to Vieta's formulas, the product of the roots p and q is given by the formula c/a.
Step 7: Conclude that if you know the coefficients a, b, and c, you can find the sum and product of the roots using these formulas.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.