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Quadratic equation problems based on properties of roots Video Lecture | Quantitative for GMAT
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FAQs on Quadratic equation problems based on properties of roots Video Lecture - Quantitative for GMAT
| 1. What are the properties of roots in a quadratic equation? |  |
Ans. The properties of roots in a quadratic equation are:
- The sum of the roots is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term.
- The product of the roots is equal to the constant term divided by the coefficient of the quadratic term.
- The roots can be real or complex depending on the discriminant of the equation.
| 2. How can I determine the sum of the roots of a quadratic equation? | |
Ans. To determine the sum of the roots of a quadratic equation, you can use the formula:
Sum of roots = -b/a, where 'a' and 'b' are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
| 3. How can I find the product of the roots of a quadratic equation? | |
Ans. To find the product of the roots of a quadratic equation, you can use the formula:
Product of roots = c/a, where 'a' and 'c' are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
| 4. What does the discriminant of a quadratic equation represent? | |
Ans. The discriminant of a quadratic equation, denoted by Δ, is a value that determines the nature of the roots. It is calculated using the formula:
Δ = b^2 - 4ac, where 'a', 'b', and 'c' are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
If Δ > 0, the equation has two distinct real roots.
If Δ = 0, the equation has two identical real roots.
If Δ < 0, the equation has two complex roots.
| 5. How can I determine if the roots of a quadratic equation are real or complex? | |
Ans. To determine if the roots of a quadratic equation are real or complex, you can check the discriminant (Δ) of the equation.
- If Δ > 0, the roots are real and distinct.
- If Δ = 0, the roots are real and identical.
- If Δ < 0, the roots are complex conjugates of each other.
About this Video
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Dec 24, 2024 Last updated |
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