Finding the Solution to a Quadratic Equation

This is an MCQ-based quiz for GRE on How To Find The Solution To A Quadratic Equation.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

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If f(x) = -x^2 + 6x - 5, then which could be the value of a if f(a) = f(1.5)?

3.5 4.5 1 4 2.5

Solve for x: 2(x + 1)^2 – 5 = 27

–2 or 4 –3 or 2 –2 or 5 3 or –5 3 or 4

Two consecutive positive multiples of three have a product of 54. What is the sum of the two numbers?

15 9 3 12 6

Solve 3x^2 + 10x = –3

x = –1/3 or –3 x = –1/6 or –6 x = –4/3 or –1 x = –1/9 or –9 x = –2/3 or –2

Solve for x: x^2 + 4x = 5

-1 or 5

-1

-5 or 1

None of the other answers

-5

Solve for x: (x^2 – x) / (x – 1) = 1

x = 1

No solution

x = 2

x = -2

x = -1

x^2 – 3x – 18 = 0

Quantity A: x
Quantity B: 6

Quantity B is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity A is greater

A farmer has 44 feet of fence, and wants to fence in his sheep. He wants to build a rectangular pen with an area of 120 square feet. Which of the following is a possible dimension for a side of the fence?

7 ft

20 ft

24 ft

10 ft

5 ft

What is the sum of all the values of that satisfy:
3x^2−5x=2x+6

2/3

14/15

7/3

4x^2+5x=3x^2−x−5
Quantity A: x
Quantity B: 1

A comparison cannot be detemined from the given information.

The two quantities are equal.