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Quadratic equation problems based on properties of roots Video Lecture | General Test Preparation for CUET - CUET Commerce

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FAQs on Quadratic equation problems based on properties of roots Video Lecture - General Test Preparation for CUET - CUET Commerce

1. What are the properties of the roots of a quadratic equation?
Ans. The properties of the roots of a quadratic equation are as follows: 1. 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. 2. The product of the roots is equal to the constant term divided by the coefficient of the quadratic term. 3. If the discriminant (b^2 - 4ac) is positive, the equation has two distinct real roots. 4. If the discriminant is zero, the equation has two identical real roots. 5. If the discriminant is negative, the equation has two complex conjugate roots.
2. How can I find the sum of the roots of a quadratic equation?
Ans. To find the sum of the roots of a quadratic equation, you can use the formula S = -b/a, where S represents the sum and 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 P = c/a, where P represents the product and a and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
4. What does it mean if a quadratic equation has two distinct real roots?
Ans. If a quadratic equation has two distinct real roots, it means that the equation can be factored into two linear factors. Each root represents a value of x where the equation equals zero, and the two roots are different from each other.
5. How do I determine the nature of the roots of a quadratic equation using the discriminant?
Ans. The discriminant, which is calculated as b^2 - 4ac, can be used to determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has two identical real roots. If the discriminant is negative, the equation has two complex conjugate roots.
155 videos|378 docs|699 tests
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