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ICSE Class 10 Quadratic Equations — practice questions

Explore 74 free Quadratic Equations questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Quadratic Equations questions and exercises with answers

Showing questions 1–30 of 74.

Order the steps of the quadratic formulaRead the answer and worked solution →Order the steps to factorise a quadraticRead the answer and worked solution →Spot the equation that does not fitRead the answer and worked solution →Standard form of a quadratic equation isRead the answer and worked solution →Which of the following is a quadratic equation?Read the answer and worked solution →The quadratic formula gives the roots of ax^2 + bx + c = 0 asRead the answer and worked solution →The quantity b^2 - 4ac is called theRead the answer and worked solution →Solve by factorisation: x^2 - 5x + 6 = 0. Roots areRead the answer and worked solution →If the roots of x^2 + bx + c = 0 are 4 and -1, then (b, c) isRead the answer and worked solution →The discriminant of 2x^2 + 5x + 3 = 0 equalsRead the answer and worked solution →Solve: x^2 = 9. The solutions areRead the answer and worked solution →Which quadratic has roots whose sum is 7 and product is 12?Read the answer and worked solution →Solve by factorisation: x^2 + 7x + 10 = 0. Roots areRead the answer and worked solution →What is the nature of the roots of x^2 + 4x + 5 = 0?Read the answer and worked solution →Solve by quadratic formula: x^2 - 4x - 5 = 0. Roots areRead the answer and worked solution →For what k does x^2 + kx + 9 = 0 have equal roots?Read the answer and worked solution →The sum of squares of two consecutive positive integers is 113. The integers areRead the answer and worked solution →If one root of x^2 - 6x + k = 0 is 2, then k equalsRead the answer and worked solution →The product of two consecutive positive odd numbers is 143. The numbers areRead the answer and worked solution →A train covers 360 km at uniform speed. If the speed were 5 km/h more, it would take 1 hour less. The actual speed isRead the answer and worked solution →If alpha and beta are roots of x^2 - 7x + 10 = 0, then alpha + beta + alpha*beta equalsRead the answer and worked solution →Solve by completing the square: x^2 + 6x + 5 = 0. Roots areRead the answer and worked solution →The area of a rectangle is 60 sq cm and length exceeds breadth by 4 cm. Breadth isRead the answer and worked solution →Roots by factoringRead the answer and worked solution →Discriminant drillRead the answer and worked solution →Quadratic or notRead the answer and worked solution →Quadratic facts, true or falseRead the answer and worked solution →The quadratic sentenceRead the answer and worked solution →Match the quadratic factsRead the answer and worked solution →Solve x² − 9x + 20 = 0 by factorisation.Read the answer and worked solution →

Worked practice questions

Order the steps of the quadratic formula

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Steps
  1. Write in standard form ax² + bx + c = 0
  2. Compute the discriminant D = b² − 4ac
  3. If D ≥ 0, real roots exist; if D < 0, roots are complex
  4. Apply x = (−b ± √D) / 2a
  5. Simplify and list both roots
Instructions
Tap the steps in order to solve a quadratic equation using the formula.

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Order the steps to factorise a quadratic

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Steps
  1. Write in standard form ax² + bx + c = 0
  2. Find two numbers that multiply to a·c and add to b
  3. Split the middle term using those numbers
  4. Factor by grouping into two binomial factors
  5. Set each factor equal to zero and solve for x
Instructions
Tap the steps in order to solve a quadratic by splitting the middle term.

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Spot the equation that does not fit

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Questions
  1. Items
    1. x² − 5x + 6 = 0
    2. x³ + x = 0
    3. 2x² + 3 = 0
    4. (x−1)(x+2) = 0
    Reason
    x³ + x = 0 is cubic; the others are quadratic in x.
    Odd item
    x³ + x = 0
Instructions
Four equations are on the board. Tap the one that does not belong with the rest.

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