If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is t
Practice Questions
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If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p? (2019)
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Questions & Step-by-Step Solutions
If the roots of the quadratic equation x^2 + px + q = 0 are -2 and -3, what is the value of p? (2019)
Step 1: Identify the roots of the quadratic equation. The roots given are -2 and -3.
Step 2: Recall that for a quadratic equation of the form x^2 + px + q = 0, the sum of the roots can be calculated using the formula: sum of roots = -p.
Step 3: Calculate the sum of the roots. Add -2 and -3 together: -2 + -3 = -5.
Step 4: Since the sum of the roots is equal to -p, we can set up the equation: -p = -5.
Step 5: To find p, multiply both sides of the equation by -1: p = 5.
Roots of Quadratic Equations – Understanding how to find the coefficients of a quadratic equation using its roots.
Sum and Product of Roots – Applying Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product is c/a.
