10 Questions
If one root of the equation x^2 + mx - 5 = 0 is 2, what is the value of m?
$-8$
What is the discriminant of the quadratic equation 2y^2 - y + 2 = 0?
$-31$
Which of the following sets of roots can form a quadratic equation?
{0, 7}
What is one possible quadratic equation for which the roots are 10 and -10?
$x^2 - 100 = 0$
For which equation do the roots have a sum of 5 and a sum of their cubes equal to 35?
$x^2 - 5x + 6 = 0$
What is the solution to the equation (m - 12)x^2 + 2(m - 12)x + 2 = 0 to have real and equal roots?
$m = -6$
If Mukund possesses `50 more than Sagar, what could be a suitable quadratic equation representing their possessions?
m(s+50) = 0
What is the nature of roots for the quadratic equation 3x^2 - 5x + 7 = 0?
Complex conjugates
Which equation has real and equal roots when solved?
x^2 - 3x +1=0
One of the roots of equation x^2 + mx - 5 = 0 is 2; find m. Which distractor correctly provides m?
-9
Study Notes
Quadratic Equations
- A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (x) is two.
- The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
Solving Quadratic Equations Using Formula
- The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
- The formula can be used to solve quadratic equations of the form ax^2 + bx + c = 0.
Nature of Roots of a Quadratic Equation
- The nature of roots of a quadratic equation depends on the value of b^2 - 4ac, which is called the discriminant (∆).
- If ∆ > 0, the roots are real and unequal.
- If ∆ = 0, the roots are real and equal.
- If ∆ < 0, the roots are not real.
Discriminant (∆)
- The discriminant (∆) is b^2 - 4ac.
- It determines the nature of roots of a quadratic equation.
Examples and Practice Exercises
- Various examples and practice exercises are provided to illustrate the concepts of quadratic equations.
- These include solving quadratic equations, finding the value of the discriminant, determining the nature of roots, and more.
Trapezium and Quadratic Equation
- A trapezium is a quadrilateral with two pairs of opposite sides.
- The area of a trapezium can be found using the formula: Area = (sum of parallel sides) * height / 2.
- A quadratic equation can be used to find the length of the parallel sides.
Problem Set
- A set of practice exercises is provided to test understanding of quadratic equations.
- The exercises cover a range of topics, including solving quadratic equations, finding the value of the discriminant, determining the nature of roots, and more.
Test your knowledge of solving quadratic equations using formulas and flow charts. Practice solving equations with different coefficients and identify the values of a, b, c to find the roots. Includes examples like x² - 7x + 5 = 0 and 2m² = 5m - 5.
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