30 Questions
What is the first step to solve a quadratic equation using the completing the square method?
Divide the equation by the coefficient of x^2
In the quadratic equation x^2 - 5x - 3 = 0, what are the roots of the equation?
x = 5 or x = -3
What is the solution to the quadratic equation x^2 + 8x - 48 = 0?
x = 4 or x = -12
For which of the following equations would completing the square method be most appropriate?
m^2 - 5m = -3
What is the intermediary step when solving x^2 + 8x - 48 = 0 using factorization?
(x + 4)^2 - 64 = 0
What is a key advantage of converting a quadratic equation to a form of difference of two squares?
Simplifies factorization of the equation
In the first example given, what is the solution for x and y in the simultaneous equations 5x - 3y = 8 and 3x + y = 2?
(x, y) = (1, -1)
Which of the following is a quadratic equation?
$x(x + 5) = 2$
What is the method used to solve the simultaneous equations in the second example given?
Addition method
Which of the following is NOT a quadratic equation?
$5x^2 = 90$
When solving 3x + 2y = 29 and 5x - y = 18, what is the correct solution for x and y?
(x, y) = (8, -3)
If the roots of $x^2 + kx + k = 0$ are real and equal, what is the value of k?
0
What is the result of multiplying equation (II) by 2 in the second example given?
-10x + 2y = 36
For $2x^2 - 5x + 2 = 0$, what is the value of the discriminant?
17
In the third example provided, what happens to the coefficients of x and y in the two equations?
They are interchanged
Which of the following quadratic equations has roots 3 and 5?
$x^2 - 8x + 15 = 0$
What is the correct value of x when solving 15x + 17y = 21 and 17x + 15y = 11?
x = -3
Out of the following equations, which one has the sum of its roots as -5?
$x^2 - x - 6 = 0$
What is the formula used to solve a quadratic equation according to the text?
$2a - b - \frac{b^2 - 4ac}{2a}$
Which expression represents one of the roots of a quadratic equation?
$-\frac{b}{2a} - \sqrt{\frac{b^2-4ac}{2a}}$
From the given text, how are the values 'a' and 'b' related?
a and b are unrelated in the context
What happens to the roots of a quadratic equation if a root is represented by 'a'?
Both roots become equal
What is the relationship between 'a', 'b', and 'c' in the context of solving a quadratic equation?
$ab = c$
How does the formula $2ax = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ help in solving quadratic equations?
It assists in finding the discriminant
In an arithmetic progression, what is the nth term formula?
$a_n = a + (n-1)d$
In an arithmetic progression, if the first term is 3 and the common difference is 5, what is the 6th term?
28
What is the sum of the first 10 terms of an arithmetic progression with a first term of 2 and a common difference of 3?
85
How many oranges would each student receive if Ranjana distributed them equally among 30 students?
20
What is the area of Mr. Dinesh's agricultural farm if the pond's area is 100 square meters?
400 square meters
If a tank fills in 2 hours with both taps open, how long does it take for the smaller tap alone to fill the tank?
8 hours
Learn how to solve quadratic equations by factoring using the formula for dividing a polynomial by a. This method involves writing the polynomial in the form of a difference of two squares to obtain the roots or solutions of the equation.
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