Problems on Quadratic Equations

We will discuss here about some of the problems on quadratic equations.

1. Solve: x^2 = 36

x^2 = 36

or, x^2 - 36=0

or, (x + 6)(x - 6) = 0

So, one of x + 6 and x - 6 must be zero

From x + 6 = 0, we get x = -6

From x - 6 = 0, we get x = 6

Thus, the required solutions are x = ± 6

Keeping the expression involving the unknown quantity and the constant term on left and right side respectively and finding square root from both sides, we can solve the equation also.

As in the equation x^2 = 36, finding square root from both sides, we get x = ± 6.


2.  Solve 2x^2 - 5x + 3 = 0

2x^2 - 5x + 3 = 0

or 2x^2 - 3x – 2x + 3=0

or, x (2x - 3) - 1 (2x - 3)=0

or, (x - 1)(2x - 3) = 0

Therefore, one of (x - 1) and (2x - 3) must be zero.

when, x - 1 = 0, x = 1

and when 2x - 3 = 0, x = 3/2

Thus required solutions are x = 1, 3/2

 

3. Solve: 3x^2 - x = 10

3x^2 - x = 10

or, 3x^2 - x - 10 = 0

or, 3x^2 - 6x + 5x - 10 = 0

or, 3x (x - 2) + 5 (x - 2) =0

or, (x - 2)(3x + 5) = 0

Therefore, one of x - 2 and 3x + 5 must be zero

When x - 2 = 0, x = 2

and when 3x + 5 = 0; 3x = -5 or; x = -5/3

Therefore, required solutions are x= -5/3, 2

 

4. Solve: (x - 7)(x - 9) = 195

(x - 7)(x - 9) = 195

or, x^2 - 9x – 7x + 63 – 195 = O

or, x2 - 16x - 132=0

or, x^2 - 22 x + 6x - 132=0

or, x(x - 22) + 6(x - 22) = 0

or, (x - 22)(x + 6) = 0

Therefore, one of x - 22 and x + 6 must be zero.

When x - 22, x = 22

when x + 6 = 0, x = - 6

Required solutions are x= -6, 22



5. Solve: x/3 +3/x =  4 1/4

or, x2 + 9/3x = 17/4

or, 4x2 + 36 = 51x

or, 4x^2 - 51x + 36 = 0

or, 4x^2 - 48x - 3x + 36 = 0

or, 4x(x- 12) -3(x - 12) = 0

or, (x - 12)(4x -3) = 0

Therefore, one of (x - 12) and (4x - 3) must be zero.

When x - 12 = 0, x = 12 when 4x -3 = 0,x = 3/4


6. Solve: x - 3/x + 3 - x + 3/x - 3 + 6 6/7 = 0

Assuming x - 3/x + 3 = a, the given equation can be written as:

a - 1/a + 6 6/7 = 0

or, a2 - 1/a + 48/7 = 0

or, a2 - 1/a = - 48/7

or, 7a^2 - 7 = - 48a

or, 7a^2 + 48a - 7 = 0

or,7a^2 + 49a - a - 7 = 0

or, 7a(a + 7) - 1 (a + 7) = 0

or,(a + 7)(7a - 1) = 0

Therefore, 0ne of (a + 7) and (7a - 1) must be zero.

a + 7 = 0 gives a = -7 and 7a - 1 = 0 gives a = 1/7

From a = -7 we get x -3/x + 3 = -7

or, x – 3 = -7x - 2 1

or, 8x = -18

Therefore, x = -18/8 = - 9/4

Again, from a = 1/7, we get x - 3/x + 3 = 1/ 7

or, 7x - 21 = x + 3

or,6x = 24

Therefore, x = 4

Required solutions are x = -9/4, 4

Quadratic Equation

Introduction to Quadratic Equation

Formation of Quadratic Equation in One Variable

Solving Quadratic Equations

General Properties of Quadratic Equation

Methods of Solving Quadratic Equations

Roots of a Quadratic Equation

Examine the Roots of a Quadratic Equation

Problems on Quadratic Equations

Quadratic Equations by Factoring

Word Problems Using Quadratic Formula

Examples on Quadratic Equations 

Word Problems on Quadratic Equations by Factoring

Worksheet on Formation of Quadratic Equation in One Variable

Worksheet on Quadratic Formula

Worksheet on Nature of the Roots of a Quadratic Equation

Worksheet on Word Problems on Quadratic Equations by Factoring








9th Grade Math

From Problems on Quadratic Equations to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More