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Andhra Pradesh SSC (Class 10) Quadratic Equations — practice questions

Explore 63 free Quadratic Equations questions in Andhra Pradesh SSC (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 63.

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?Read the answer and worked solution →For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?Read the answer and worked solution →Find the roots of $2x^2-5x+3=0$ by factorisation.Read the answer and worked solution →What is the maximum number of real roots a quadratic equation can have?Read the answer and worked solution →If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\neq 0$, then which statement must be true?Read the answer and worked solution →Which equation appears cubic at first glance but actually simplifies to a quadratic equation?Read the answer and worked solution →Which of the following is NOT a quadratic equation after simplification?Read the answer and worked solution →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 →

Worked practice questions

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?

  1. The equation has two distinct real roots
  2. The equation has two equal real roots
  3. The equation has no real roots
  4. The equation has exactly one real root
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Correct answer: C. The equation has no real roots

If $b^2-4ac<0$, then the square root term in the quadratic formula is not a real number. **Therefore, the quadratic equation has no real roots.**

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

  1. $b^2+4ac$
  2. $4ac-b^2$
  3. $b^2-4ac$
  4. $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Show answer and solution

Correct answer: C. $b^2-4ac$

The discriminant of the quadratic equation $ax^2+bx+c=0$ is the expression under the square root in the quadratic formula, namely $b^2-4ac$. It determines the nature of the roots.

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Find the roots of $2x^2-5x+3=0$ by factorisation.

  1. $x=\frac{3}{2},\ 1$
  2. $x=\frac{5}{2},\ 3$
  3. $x=-\frac{3}{2},\ -1$
  4. $x=\frac{2}{3},\ 1$
Show answer and solution

Correct answer: A. $x=\frac{3}{2},\ 1$

Factorise $2x^2-5x+3$ by splitting the middle term: $2x^2-2x-3x+3=2x(x-1)-3(x-1)=(2x-3)(x-1)$. So $(2x-3)(x-1)=0$, giving $2x-3=0$ or $x-1=0$. **Hence the roots are $x=\frac{3}{2}$ and $x=1$.**

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More Mathematics topics

Real Numbers and PolynomialsArithmetic ProgressionStatistics and ProbabilityLinear Equations in Two VariablesTriangles and CirclesIntroduction to TrigonometrySurface Areas and VolumesAreas Related to Circles