Algebra · Practice

Quadratic Equations — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

Solve by factoring and enter the larger root: x2−5x+6=0\quad x^2 - 5x + 6 = 0

Problem 2

Enter the positive root: x2−9=0\quad x^2 - 9 = 0

Problem 3

Solve: x2+6x+9=0\quad x^2 + 6x + 9 = 0

Problem 4

A ball is thrown upward with height h(t)=−5t2+20th(t) = -5t^2 + 20t metres. After how many seconds does it hit the ground?

Intermediate

Problem 5

Enter the larger root: 2x2−7x+3=0\quad 2x^2 - 7x + 3 = 0

Problem 6

Use the quadratic formula. Enter the larger root: x2+4x−12=0\quad x^2 + 4x - 12 = 0

Problem 7

For what value of kk does x2−6x+k=0x^2 - 6x + k = 0 have exactly one real solution?

Problem 8

A rectangle has area 4848 and its length is 22 more than its width. Find the width.

Advanced

Problem 9

Enter the larger root to 2 decimal places: x2−2x−1=0\quad x^2 - 2x - 1 = 0

Problem 10

How many real roots does x2−3x−10=0x^2 - 3x - 10 = 0 have in total?

Problem 11

Two positive numbers sum to 1010. What is the maximum value of their product?