Podcast
Questions and Answers
Which of the following quadratic equations has real roots?
Which of the following quadratic equations has real roots?
What are the values of $k$ in the quadratic equation $2x^2 + kx + 3 = 0$ that will result in two equal roots?
What are the values of $k$ in the quadratic equation $2x^2 + kx + 3 = 0$ that will result in two equal roots?
Is it possible for two friends to have a sum of ages of 20 years, where four years ago, the product of their ages was 48? If so, what are their present ages?
Is it possible for two friends to have a sum of ages of 20 years, where four years ago, the product of their ages was 48? If so, what are their present ages?
Is it possible to design a rectangular mango grove with an area of 800 m², where the length is twice the breadth? If so, what are the length and breadth?
Is it possible to design a rectangular mango grove with an area of 800 m², where the length is twice the breadth? If so, what are the length and breadth?
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Is it possible to design a rectangular park with a perimeter of 80 m and an area of 400 m²? If so, what are the length and breadth of the park?
Is it possible to design a rectangular park with a perimeter of 80 m and an area of 400 m²? If so, what are the length and breadth of the park?
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Which of the following is the correct form of a quadratic equation?
Which of the following is the correct form of a quadratic equation?
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Which of the following equations has real roots?
Which of the following equations has real roots?
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What are the values of $k$ in the equation $kx(x - 2) + 6 = 0$ that will result in two equal roots?
What are the values of $k$ in the equation $kx(x - 2) + 6 = 0$ that will result in two equal roots?
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Is it possible to design a rectangular park with a perimeter of 80 m and an area of 400 m²? If so, what are the length and breadth of the park?
Is it possible to design a rectangular park with a perimeter of 80 m and an area of 400 m²? If so, what are the length and breadth of the park?
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Is it possible to design a rectangular mango grove with an area of 800 m², where the length is twice the breadth? If so, what are the length and breadth?
Is it possible to design a rectangular mango grove with an area of 800 m², where the length is twice the breadth? If so, what are the length and breadth?
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Study Notes
Quadratic Equations
- A quadratic equation has real roots if the discriminant (b² - 4ac) is greater than or equal to 0.
Solving Quadratic Equations
- The quadratic equation 2x² + kx + 3 = 0 has two equal roots if k² - 4(2)(3) = 0.
Age Problems
- It is possible for two friends to have a sum of ages of 20 years, where four years ago, the product of their ages was 48.
- To find the present ages, let the ages be x and 20 - x, and the ages four years ago be x - 4 and 20 - x - 4.
Rectangular Shapes
- It is possible to design a rectangular mango grove with an area of 800 m², where the length is twice the breadth.
- Let the breadth be x, then the length is 2x, and the area is x(2x) = 800.
Perimeter and Area of Rectangular Shapes
- It is possible to design a rectangular park with a perimeter of 80 m and an area of 400 m².
- Let the length and breadth be l and b, then the perimeter is 2(l + b) = 80, and the area is lb = 400.
Quadratic Equation Forms
- The correct form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.
Solving Equations
- The equation kx(x - 2) + 6 = 0 has two equal roots if k² - 4(k)(6) = 0.
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Description
Test your knowledge of quadratic equations and their roots with this quiz. Determine the nature of the roots and find the real roots if they exist. Additionally, solve for the values of k in quadratic equations to find two equal roots. Can you design a rectangular mango grove? Find out with this quiz!
