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  1. Problems
  2. /Algebra
  3. /Quadratic Equations

Quadratic Equations

Mathematics
+ Upload a Problem
More in AlgebraLinear Equations in Two VariablesPairs of Linear EquationsPolynomialsAlgebraic Identities and FactorisationQuadratic EquationsSequences and SeriesLinear InequalitiesComplex NumbersPermutations and CombinationsBinomial TheoremMatrices and Determinants
22 problems
Type:
1.
Show that there is no real number k for which x² + 2(k + 3)x + 9k = 0 has two equal roots. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Hard
2.
A rectangular hall must have a perimeter of 52 m. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
3.
Find the values of k for which (k + 1)x² - 2(k - 1)x + 1 = 0 has two equal roots. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
4.
Find the discriminant of each equation and say what kind of roots it has. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
5.
A stone is thrown upwards. After t seconds its height is h = 30t - 5t² metres. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Hard
6.
Arjun cycles 36 km to his grandmother's house. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
7.
A rectangular field is 3 m longer than it is wide, and its area is 50 m². New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
8.
Solve 2x² + 3x - 7 = 0 with the quadratic formula. Give the roots to 2 decimal places. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
9.
Show, by completing the square, that x² - 6x + 11 is greater than zero for every real number x. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
10.
Solve 3x² + 12x - 5 = 0 by completing the square. Give the roots to 2 decimal places. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
11.
Solve x² + 8x - 20 = 0 by completing the square. Check both roots. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
12.
Meera's age two years ago, multiplied by her age five years from now, gives 98. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Hard
13.
A cyclist rides 60 km. If she rode 5 km/h faster, the ride would take 1 hour less. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
14.
The floor of a hall is a rectangle 4 m longer than it is wide. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
15.
The product of two consecutive positive even numbers is 168. Find the numbers. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
16.
Solve 2x² - 2√2 x + 1 = 0. Give the root to two decimal places. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Hard
17.
Tanvi solves x² = 7x like this: "Divide both sides by x, so x = 7." Explain her mistake, and find… New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
18.
Solve 6x² + x - 15 = 0 by splitting the middle term. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
19.
Solve x² - 9x + 20 = 0 by factorisation. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
20.
Is x = 2/3 a root of 3x² + 7x - 6 = 0? For what value of k is x = 2 a root of kx² - 3x - 10 = 0? New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Medium
21.
Each side of a square plot is x metres. When each side is made 3 m longer, the area becomes 81 m². New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy
22.
Which of these are quadratic equations? Give a reason for each. New
High School (9–10), General · Quadratic EquationsStemPy LabStemPy Lab
Easy