Questions and Answers
Which of the following quadratic equations has real roots?
$2x^2 - 3x + 5 = 0$
What are the values of $k$ in the quadratic equation $2x^2 + kx + 3 = 0$ that will result in two equal roots?
$k = 0$
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?
Yes, one friend is 8 years old and the other is 12 years old
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?
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Which of the following is the correct form of a quadratic equation?
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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?
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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?
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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?
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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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