If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is t
Practice Questions
Q1
If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is the value of c if a = 1 and b = -1?
-6
6
5
1
Questions & Step-by-Step Solutions
If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is the value of c if a = 1 and b = -1?
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and -2.
Step 2: Recall that for a quadratic equation in the form ax^2 + bx + c = 0, the product of the roots (r1 and r2) is given by the formula r1 * r2 = c/a.
Step 3: Since a = 1, we can simplify the formula to r1 * r2 = c.
Step 4: Calculate the product of the roots: 3 * (-2) = -6.
Step 5: Therefore, c = -6.
Roots of Quadratic Equations – Understanding how to find the coefficients of a quadratic equation using its roots.
Vieta's Formulas – Applying Vieta's formulas to relate the coefficients of a polynomial to sums and products of its roots.
Quadratic Coefficients – Identifying the relationship between the coefficients a, b, and c in a quadratic equation.
