Quadratic Equations Questions and Answers

Questions on Quadratic Equations

If you’re looking to master quadratic equations, understanding and practicing various questions on this topic is essential. Quadratic equations are second-degree polynomial equations with the general form ax^2 + bx + c = 0, where ‘a’, ‘b’, and ‘c’ are constants. These equations have two solutions, called roots, which can be found using methods like factoring, completing the square, or using the quadratic formula.

Quadratic Equation Questions

Methods for finding roots of Quadratic Equation

The roots or solutions of a quadratic equation are the values of ‘x’ that satisfy the equation, making it true. A quadratic equation can have two real roots, two complex roots, or one real root (in case of a perfect square). The number of roots is determined by the value of the discriminant (Δ) given by:

Δ = b^{2}-4ac

  1. If Δ > 0, the quadratic equation has two distinct real roots.
  2. If Δ = 0, the quadratic equation has one real root (repeated or equal roots).
  3. If Δ < 0, the quadratic equation has two complex roots (conjugate pairs).

To find the roots of a quadratic equation, several methods can be used:

  1. Factoring: If the equation can be factored, the roots can be directly determined from the factors.

  2. Quadratic Formula: The quadratic formula is a general method to find the roots of any quadratic equation and is given by:

    x = \frac{(-b\pm \sqrt{b^{2}-4ac})}{2a}

    where the ± sign accounts for the two possible solutions.

  3. Completing the Square: This method involves transforming the quadratic equation into a perfect square form, from which the roots can be easily obtained.

Rules for Quadratic Equations

  • If p+ √q is a root of a quadratic equation, then its other root is p-√q.
  • When D ≥ 0, then rx^2+ dx + z can be expressed as a product of two linear factors.
  • If α and β are the roots of rx^2+ dx + z, then we can write it as: x^2 – (α + β)x + α β = 0.

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Question 1

Time: 00:00:00
Calculate the number of real roots of the quadratic equation a^{2}+5a+6= 0 ?

7

7

1

1

4

4

2

2

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Question 2

Time: 00:00:00
Calculate the number of real roots of the equation a^{4}+ a^{2}+1= 0

2

2

-3

-3

-2

-2

None

None

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Question 3

Time: 00:00:00
Calculate the number of distinct real roots of the equation p^{11}+7p^{3}-5=0

-3

-3

1

1

-6

-6

2

2

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Question 4

Time: 00:00:00
Calculate the value of p when the equation a^{2}-(p+6) a+2(2p-1)= 0 if the total of roots equals half their product?

7

7

-7/3

-7/3

1

1

zero

zero

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Question 5

Time: 00:00:00
Which of the following is a quadratic equation?

x³ + 2x + 1 = x² + 3

x³ + 2x + 1 = x² + 3

– 2x = (5 – x) (2x – 25)

– 2x = (5 – x) (2x – 25)

( k + 1 )x² +32x=7, where k = -1

( k + 1 )x² +32x=7, where k = -1

x³x² = (x³)

x³x² = (x³)

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Question 6

Time: 00:00:00
Which of the following is the solution to the inequality 2x^2 + 5x - 3 > 0?

x > 3/2 or x < -1

x > 3/2 or x < -1

x > 3/2 and x < -1

x > 3/2 and x < -1

x > -3/2 and x < 1

x > -3/2 and x < 1

x < -3 and x > 1/2

x < -3 and x > 1/2

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Question 7

Time: 00:00:00
Calculate the sum of roots of the below mentioned quadratic equation:

3a^{2}+2a-1= 0.

−2/3

−2/3

1/4

1/4

7/3

7/3

-5/6

-5/6

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Question 8

Time: 00:00:00
Calculate the product of roots of the below mentioned quadratic equation:

3a^{2}+2a-1= 0.

2/3

2/3

zero

zero

-1/3

-1/3

1/7

1/7