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Uttarakhand Board Class 10 Quadratic Equations — practice questions

Explore 48 free Quadratic Equations questions in Uttarakhand Board 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 48.

The standard form of a quadratic equation in the variable x is:Read the answer and worked solution →For a quadratic equation $ax^2+bx+c=0$, the discriminant is:Read the answer and worked solution →A quadratic equation has two distinct real roots when its discriminant is:Read the answer and worked solution →A quadratic equation has two equal real roots when its discriminant is:Read the answer and worked solution →A quadratic equation has no real roots when its discriminant is:Read the answer and worked solution →For $ax^2+bx+c=0$, the sum of the roots equals:Read the answer and worked solution →For $ax^2+bx+c=0$, the product of the roots equals:Read the answer and worked solution →The roots of the equation $x^2 - 5x + 6 = 0$ are:Read the answer and worked solution →The roots of $x^2 + 4x + 4 = 0$ are:Read the answer and worked solution →The value(s) of k for which $x^2 + kx + 9 = 0$ has two equal roots is/are:Read the answer and worked solution →The discriminant of $2x^2 - 4x + 3 = 0$ is −8, so the equation has:Read the answer and worked solution →A quadratic equation can have at most how many roots?Read the answer and worked solution →Which of the following is a quadratic equation?Read the answer and worked solution →For ax² + bx + c = 0 to be a quadratic equation, what condition must hold?Read the answer and worked solution →Is x = 3 a root of the equation x² − 4x + 3 = 0?Read the answer and worked solution →A rectangular field is 5 m longer than it is wide, and its area is 50 m². If the width is x metres, which equation describes x?Read the answer and worked solution →Identify a, b, c in the equation 3x² − 7x + 2 = 0.Read the answer and worked solution →Solve x² − 5x + 6 = 0 by factorisation.Read the answer and worked solution →Solve x² + 7x + 12 = 0.Read the answer and worked solution →Solve 2x² + 7x + 3 = 0.Read the answer and worked solution →Solve x² − 8x + 16 = 0.Read the answer and worked solution →The roots of x² − x − 12 = 0 are:Read the answer and worked solution →A rectangular plot has its length 3 m more than its width, and its area is 54 m². Find its width.Read the answer and worked solution →For ax² + bx + c = 0, the discriminant is:Read the answer and worked solution →For x² + 4x + 13 = 0, find the discriminant and classify roots.Read the answer and worked solution →For x² − 6x + 9 = 0, find D and the nature of roots.Read the answer and worked solution →Solve 2x² − 5x + 3 = 0 by the quadratic formula.Read the answer and worked solution →For what value of k does x² + kx + 16 = 0 have equal roots?Read the answer and worked solution →Solve x² − 2x − 4 = 0.Read the answer and worked solution →Complete the definition of slopeRead the answer and worked solution →

Worked practice questions

The standard form of a quadratic equation in the variable x is:

  1. $ax^2 + bx + c = 0,\ a \neq 0$
  2. $ax^3 + bx^2 + c = 0$
  3. $ax^2 + bx = 0,\ b \neq 0$
  4. $ax + b = 0,\ a \neq 0$
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Correct answer: A. $ax^2 + bx + c = 0,\ a \neq 0$

Standard form: ax²+bx+c=0 with a≠0.

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For a quadratic equation $ax^2+bx+c=0$, the discriminant is:

  1. $4ac - b^2$
  2. $b^2 - 4ac$
  3. $b^2 + 4ac$
  4. $\sqrt{b^2-4ac}$
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Correct answer: B. $b^2 - 4ac$

Discriminant D = b²−4ac determines the nature of roots.

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A quadratic equation has two distinct real roots when its discriminant is:

  1. equal to one
  2. less than zero
  3. greater than zero
  4. equal to zero
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Correct answer: C. greater than zero

D > 0 → two distinct real roots.

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More Mathematics topics

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