Choose the correct answer from the given four options in the following questions: $\left(x^2+1\right)^2-x^2=0$ has:
- AFour real roots.
- BTwo real roots.
- ✓No real roots.
- DOne real root.
Answer: C.
View full solution →Question types
Quadratic Equations question types
50 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
50
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
11 Q→021 Marks Question
2 Q→032 Marks Questions
11 Q→043 Marks Question
18 Q→055 Marks Questions
8 Q→Sample Questions
Quadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Choose the correct answer from the given four options in the following questions:
Which constant must be added and subtracted to solve the quadratic equation $9\text{x}^2+\frac{3}{4}\text{x}-\sqrt{2}=0$ by the method of completing the square?
Which constant must be added and subtracted to solve the quadratic equation $9\text{x}^2+\frac{3}{4}\text{x}-\sqrt{2}=0$ by the method of completing the square?
- A$\frac{1}{8}$
- ✓$\frac{1}{64}$
- C$\frac{1}{4}$
- D$\frac{9}{64}$
Answer: B.
View full solution →Choose the correct answer from the given four options in the following questions: Values of $k$ for which the quadratic equation $2x^2 - kx + k = 0$ has equal roots is:
- A$0$ only.
- B$4.$
- C$8$ only.
- ✓$0, 8.$
Answer: D.
View full solution →Choose the correct answer from the given four options in the following questions:
The quadratic equation $2\text{x}^2-\sqrt{5}\text{x}+1=0$ has.
The quadratic equation $2\text{x}^2-\sqrt{5}\text{x}+1=0$ has.
- ATwo distinct real roots.
- BTwo equal real roots.
- ✓No real roots.
- DMore than 2 real roots.
Answer: C.
View full solution →Choose the correct answer from the given four options in the following questions:
Which of the following equations has the sum of its roots as $3?$
Which of the following equations has the sum of its roots as $3?$
- A$2\text{x}^2-3\text{x}+6=0.$
- ✓$-\text{x}^2+3\text{x}-3=0.$
- C$\sqrt{2}\text{x}^2-\frac{3}{\sqrt{2}}\text{x}+1=0.$
- D$3\text{x}^2-3\text{x}+3=0$
Answer: B.
View full solution →State whether the following quadratic equations have two distinct real roots. Justify your answer.
$\big(\text{x}-\sqrt{2}\big)^2-2(\text{x}+1)=0.$
View full solution →$\big(\text{x}-\sqrt{2}\big)^2-2(\text{x}+1)=0.$
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$x(1 - x) - 2 = 0.$
View full solution →$x(1 - x) - 2 = 0.$
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$(x - 1)(x + 2) + 2 = 0.$
View full solution →$(x - 1)(x + 2) + 2 = 0.$
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$x2 - 3x + 4 = 0$
View full solution →$x2 - 3x + 4 = 0$
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$(x + 1)(x - 2) + x = 0.$
View full solution →$(x + 1)(x - 2) + x = 0.$
State whether the following quadratic equations have two distinct real roots. Justify your answer.
$(x + 4)^2 - 8x = 0.$
View full solution →$(x + 4)^2 - 8x = 0.$
Find whether the following equations have real roots. If real roots exist, find them.
$5x^2 - 2x - 10 = 0.$
View full solution →$5x^2 - 2x - 10 = 0.$
Find a natural number whose square diminished by $84$ is equal to thrice of 8 more than the given number.
View full solution →Find the roots of the following quadratic equations by the factorisation method:
$3\sqrt{2}\text{x}^2-5\text{x}-\sqrt{2}=0.$
View full solution →$3\sqrt{2}\text{x}^2-5\text{x}-\sqrt{2}=0.$
Find whether the following equations have real roots. If real roots exist, find them.
$8x^2 + 2x - 3 = 0.$
View full solution →$8x^2 + 2x - 3 = 0.$
Find whether the following equations have real roots. If real roots exist, find them.
$-2x^2 + 3x + 2 = 0.$
View full solution →$-2x^2 + 3x + 2 = 0.$
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
Find the roots of the quadratic equations by using the quadratic formula in each of the following:
$\text{x}^2+2\sqrt{2}\text{x}-6=0.$
View full solution →$\text{x}^2+2\sqrt{2}\text{x}-6=0.$
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Find whether the following equations have real roots. If real roots exist, find them.
$\frac{1}{2\text{x}-3}+\frac{1}{\text{x}-5}=1,\text{x}\neq\frac{3}{2},5.$
View full solution →$\frac{1}{2\text{x}-3}+\frac{1}{\text{x}-5}=1,\text{x}\neq\frac{3}{2},5.$
In the centre of a rectangular lawn of dimensions 50m × 40m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184m^2$. Find the length and breadth of the pond.
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