Class10 Quiz Level 2 (Moderate) – Quadratic Equations

Total questions: 20

Solve the equation $\displaystyle 2{{x}^{2}}+7x+3=0$ using the quadratic formula.

Topic: Quadratic Formula Application

Deselect Answer

$ \displaystyle x=\frac{{-7\pm \sqrt{{25}}}}{4}$

$ \displaystyle x=\frac{{7\pm \sqrt{{25}}}}{4}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{49}}}}{4}$

$ \displaystyle x=\frac{{7\pm \sqrt{{49}}}}{4}$

None

The discriminant of a quadratic equation is positive ,what can be inferred about the roots?

Topic: Nature of Roots

Deselect Answer

The roots are real and distinct

The roots are real and equal

The roots are real and imaginary

The roots are real equal

None

The sum of the roots of the quadratic equation $ \displaystyle 2{{x}^{2}}+3x-5=0$ is ?

Topic: Sum of Roots

Deselect Answer

$ \displaystyle -\frac{3}{2}$

$ \displaystyle \frac{3}{2}$

$ \displaystyle -\frac{5}{2}$

$ \displaystyle \frac{5}{2}$

None

The vertex of the parabola $ \displaystyle y={{x}^{2}}-6x+8$ lies on which axis?

Topic: Vertex and Axis of Symmetry

Deselect Answer

x-axis

y-axis

Line 𝑥 = 3

Line y = 8

None

Factorize the quadratic expression $ \displaystyle 6{{x}^{2}}+11x-10$ .

Topic: Factorization

Deselect Answer

$\displaystyle \left( {3x+5} \right)\left( {2x-2} \right)$

$ \displaystyle \left( {3x-5} \right)\left( {2x+2} \right)$

$ \displaystyle \left( {3x+5} \right)\left( {2x-4} \right)$

$ \displaystyle \left( {3x-2} \right)\left( {2x+5} \right)$

None

What is the product of the roots of the equation $ \displaystyle 4{{x}^{2}}-5x+1=0$ ?

Topic: Product of Roots

Deselect Answer

$ \displaystyle \frac{1}{4}$

$ \displaystyle -\frac{1}{4}$

None

The graph of $ \displaystyle y={{x}^{2}}+4x+k$ touches the x-axis at exactly one point. what is the value of k?

Topic: Graphs of Quadratic Functions

Deselect Answer

-4

None

If the roots of the quadratic equation $ \displaystyle {{x}^{2}}$ + p𝑥 + q =0 are real and equal , which of the following must be true?

Topic: Nature of Roots

Deselect Answer

$ \displaystyle {{p}^{2}}=4q$

$ \displaystyle {{p}^{2}}<4q$

$ \displaystyle {{p}^{2}}>4q$

$\displaystyle p=4q$

None

Find the roots the equation $ \displaystyle 3{{x}^{2}}+7x-2=0$ using the quadratic formula?

Topic: Roots of a Quadratic Equations

Deselect Answer

$ \displaystyle x=\frac{{-7\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{49}}}}{6}$

$ \displaystyle x=\frac{{7\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\frac{{-7\pm \sqrt{{29}}}}{6}$

None

10.

The vertex of the parabola $ \displaystyle y={{x}^{2}}-6x+8$ lies on which axis?

Deselect Answer

x-axis

y-axis

Line 𝑥 = 3

Line y = 8

None

11.

If one of the roots of the quadratic equation $ \displaystyle {{x}^{2}}+7x+p=0$ is -3 , what is the value of p?

Topic: Roots of a Quadratic Equations

Deselect Answer

None

12.

For what value of k does the quadratic equation $ \displaystyle 2{{x}^{2}}-kx+3=0$ have equal roots?

Topic: Nature of Roots

Deselect Answer

$ \displaystyle k=\sqrt{{24}}$

k = 24

$ \displaystyle k=2\sqrt{6}$

k = 12

None

13.

Factorize the quadratic expression $ \displaystyle 3{{x}^{2}}+7x+2$ .

Topic: Factorization

Deselect Answer

$ \displaystyle \left( {3x+1} \right)\left( {x+2} \right)$

$ \displaystyle \left( {3x+2} \right)\left( {x+1} \right)$

$ \displaystyle \left( {3x-1} \right)\left( {x+2} \right)$

$ \displaystyle \left( {3x+1} \right)\left( {x+1} \right)$

None

14.

If the sum of the roots of a quadratic equation $ \displaystyle 3{{x}^{2}}+bx+c=0$ is 5 and the product of the roots is 2 ,what are the value of b and c?

Topic: Sum and product of Roots

Deselect Answer

$ \displaystyle b=-15,c=6$

$ \displaystyle b=-5,c=6$

$ \displaystyle b=-5,c=2$

$ \displaystyle b=-15,c=2$

None

15.

Solve the quadratic equation $ \displaystyle {{x}^{2}}-5x+6=0$ by factorization. What are the roots?

Topic: Solving Quadratic Equations

Deselect Answer

3 and 2

6 and -1

1 and 6

-3 and 2

None

16.

The system of equations $ \displaystyle 3x+4y=7\text{ and 6}x+8y=k$ has infinitely many solutions if:

Deselect Answer

$ \displaystyle k=7$

$ \displaystyle k=14$

$ \displaystyle k=21$

$ \displaystyle k=10$

None

17.

Using the quadratic formula, solve $ \displaystyle 3{{x}^{2}}+5x-2=0$ , what are the roots?

Topic: Quadratic Formula Application

Deselect Answer

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{49}}}}{6}$

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{25}}}}{6}$

$\displaystyle x=\dfrac{{5\pm \sqrt{{25}}}}{6}$

$ \displaystyle x=\dfrac{{5\pm \sqrt{{49}}}}{6}$

None

18.

Find the maximum value of the quadratic equation function $ \displaystyle y=2{{x}^{2}}-4x+1$ .

Topic: Maximum and Minimum Value

Deselect Answer

-1

-3

None

19.

Solve the quadratic equation $\displaystyle 2{{x}^{2}}-3x-2=0$ using the quadratic formula. What are the roots?

Topic: Quadratic Formula Application

Deselect Answer

$ \displaystyle x=\dfrac{{-3\pm \sqrt{{17}}}}{4}$

$ \displaystyle x=\dfrac{{3\pm \sqrt{{17}}}}{4}$

$ \displaystyle x=\dfrac{{3\pm \sqrt{{13}}}}{4}$

$ \displaystyle x=\dfrac{{-3\pm \sqrt{{13}}}}{4}$

None

20.

The system of equations $ \displaystyle {{x}^{2}}+{{y}^{2}}=25$ and $ \displaystyle x-y=7$ has:

Deselect Answer

One solution

Two solutions

No solution

Infinite solutions

None

1 out of 20

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Class10 Quiz Level 2 (Moderate) – Quadratic Equations

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