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Introduction: Quadratic Equations Video Lecture | Crash Course: Class 10

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FAQs on Introduction: Quadratic Equations Video Lecture - Crash Course: Class 10

1. What is a quadratic equation?
Ans. A quadratic equation is a polynomial equation of the second degree, in which the highest power of the variable is 2. It can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
2. How do you solve a quadratic equation by factoring?
Ans. To solve a quadratic equation by factoring, follow these steps: 1. Rewrite the equation in the form ax^2 + bx + c = 0. 2. Factor the quadratic expression on the left side of the equation. 3. Set each factor equal to zero and solve the resulting linear equations. 4. Find the values of x that satisfy the original equation by substituting the solutions from step 3 back into the equation.
3. Can a quadratic equation have more than two solutions?
Ans. No, a quadratic equation can have at most two solutions. This is because a quadratic equation is of the second degree and can be represented by a parabola, which can intersect the x-axis at most twice. The solutions can be real or complex, but there will be at most two distinct solutions.
4. What is the quadratic formula and how is it used to solve quadratic equations?
Ans. The quadratic formula is used to solve quadratic equations that cannot be easily factored. It states that for a quadratic equation ax^2 + bx + c = 0, the solutions for x can be found using the formula: x = (-b ± √(b^2 - 4ac)) / (2a) By substituting the values of a, b, and c from the given quadratic equation into the formula, we can find the solutions for x.
5. What is the discriminant of a quadratic equation and how does it determine the nature of the solutions?
Ans. The discriminant of a quadratic equation is the expression b^2 - 4ac, which is found in the quadratic formula. It determines the nature of the solutions as follows: 1. If the discriminant is positive (b^2 - 4ac > 0), the quadratic equation has two distinct real solutions. 2. If the discriminant is zero (b^2 - 4ac = 0), the quadratic equation has one real solution (also known as a double root). 3. If the discriminant is negative (b^2 - 4ac < 0), the quadratic equation has two complex solutions (conjugate pairs) that involve the imaginary unit i.
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