(K + 1)X2 - 2(3k + 1)X + 8k + 1 = 0 - Mathematics

English0CBSEEnglish Medium Class 10Question PapersQuestion Papers1484Textbook Solutions33761MCQ Online Mock Tests19Important Solutions16679Concept Notes & Videos259Time Tables17SyllabusFind the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: (K + 1)X2 - 2(3k + 1)X + 8k + 1 = 0 - Mathematics

Advertisements

Advertisements

Question

Find the values of k for which the roots are real and equal in each of the following equation:

(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0

Advertisements

SolutionShow Solution

The given quadric equation is (k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0, and roots are real and equal

Then find the value of k.

Here,

a = k + 1, b = -2(3k + 1)x and c = 8k + 1

As we know that D = b2 - 4ac

Putting the value of a = k + 1, b = -2(3k + 1)x and c = 8k + 1

= (-2(3k + 1))2 - 4 x (k + 1) x (8k + 1)

= 4(9k2 + 6k + 1) - 4(8k2 + 9k + 1)

= 36k2 + 24k + 4 - 32k2 - 36k - 4

= 4k2 - 12k

The given equation will have real and equal roots, if D = 0

4k2 - 12k = 0

k2 - 3k = 0

Now factorizing of the above equation

k(k - 3) = 0

So, either

k = 0

Or

k - 3 = 0

k = 3

Therefore, the value of k = 0, 3.

shaalaa.comNature of Roots of a Quadratic Equation Report Error Is there an error in this question or solution?Q 2.13Q 2.12Q 2.14Chapter 4: Quadratic Equations - Exercise 4.6 [Page 41]

APPEARS IN

RD Sharma Mathematics [English] Class 10Chapter 4 Quadratic EquationsExercise 4.6 | Q 2.13 | Page 41

Video TutorialsVIEW ALL [7]

• view Video Tutorials For All Subjects
• Nature of Roots of a Quadratic Equationvideo tutorial00:26:19
• Nature of Roots of a Quadratic Equationvideo tutorial00:11:20
• Nature of Roots of a Quadratic Equationvideo tutorial00:25:30
• Nature of Roots of a Quadratic Equationvideo tutorial00:20:52
• Nature of Roots of a Quadratic Equationvideo tutorial00:08:39
• Nature of Roots of a Quadratic Equationvideo tutorial00:39:17
• Nature of Roots of a Quadratic Equationvideo tutorial01:02:00

RELATED QUESTIONS

Find the values of k for which the roots are real and equal in each of the following equation:

(k + 1)x2 - 2(k - 1)x + 1 = 0

Find the value of the discriminant in the following quadratic equation:

2x2 - 3x + 1 = O

Determine the nature of the roots of the following quadratic equation :

x2 +3x+1=0

Solve the following quadratic equation using formula method only

`3"x"^2 + 2 sqrt 5x - 5 = 0 `

Solve the following quadratic equation using formula method only

25x2 + 30x + 7 = 0

Solve the following quadratic equation using formula method only

`2"x"^2- 2 sqrt 6 + 3 = 0`

Determine, if 3 is a root of the given equation`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.

Find the value of k for which the following equation has equal roots:(k − 12)x2 + 2(k − 12)x + 2 = 0.

Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.

In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1

In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`

If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case

Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.

State whether the following quadratic equation have two distinct real roots. Justify your answer.

(x + 4)2 – 8x = 0

Find the roots of the quadratic equation by using the quadratic formula in the following:

`1/2x^2 - sqrt(11)x + 1 = 0`

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.

If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.

Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.

The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.

Prove that 2q = p + r; i.e., p, q, and r are in A.P.

Question Bank with Solutions

• Maharashtra State Board Question Bank with Solutions (Official)

Textbook Solutions

• Balbharati Solutions (Maharashtra)
• Samacheer Kalvi Solutions (Tamil Nadu)
• NCERT Solutions
• RD Sharma Solutions
• RD Sharma Class 10 Solutions
• RD Sharma Class 9 Solutions
• Lakhmir Singh Solutions
• TS Grewal Solutions
• ICSE Class 10 Solutions
• Selina ICSE Concise Solutions
• Frank ICSE Solutions
• ML Aggarwal Solutions

NCERT Solutions

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for Class 12 Chemistry
• NCERT Solutions for Class 12 Biology
• NCERT Solutions for Class 11 Maths
• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Biology
• NCERT Solutions for Class 10 Maths
• NCERT Solutions for Class 10 Science
• NCERT Solutions for Class 9 Maths
• NCERT Solutions for Class 9 Science

Board / University Study Material

• CBSE Study Material
• Maharashtra State Board Study Material
• Tamil Nadu State Board Study Material
• CISCE ICSE / ISC Study Material
• Mumbai University Engineering Study Material

Question Paper Solutions

• CBSE Previous Year Question Papers With Solutions for Class 12 Arts
• CBSE Previous Year Question Papers With Solutions for Class 12 Commerce
• CBSE Previous Year Question Papers With Solutions for Class 12 Science
• CBSE Previous Year Question Papers With Solutions for Class 10
• Maharashtra State Board Previous Year Question Papers With Solutions for Class 12 Arts
• Maharashtra State Board Previous Year Question Papers With Solutions for Class 12 Commerce
• Maharashtra State Board Previous Year Question Papers With Solutions for Class 12 Science
• Maharashtra State Board Previous Year Question Papers With Solutions for Class 10
• CISCE ICSE / ISC Board Previous Year Question Papers With Solutions for Class 12 Arts
• CISCE ICSE / ISC Board Previous Year Question Papers With Solutions for Class 12 Commerce
• CISCE ICSE / ISC Board Previous Year Question Papers With Solutions for Class 12 Science
• CISCE ICSE / ISC Board Previous Year Question Papers With Solutions for Class 10

Other Resources

• Entrance Exams
• Video Tutorials
• Question Papers
• Question Bank Solutions
• Question Search (beta)
• Privacy Policy
• Terms and Conditions
• Contact Us
• About Us
• Shaalaa App
• Ad-free Subscriptions

© 2026 Shaalaa.com | Contact Us | Privacy PolicyShare 0 0 0 0 0Notifications

Select a course

CANCELEnglishहिंदीमराठीuserLoginCreate free accountemail:password:Log in Forgot password?CourseEnglish Medium Class 10 CBSEKarnataka SSLC SSLC 10th Karnataka Boardchange

• Home
• Class 1 - 4
• Class 5 - 8
• Class 9 - 10
• Class 11 - 12
• Entrance Exams
• Search by Text or Image
• Textbook Solutions
• Study Material
• Remove All Ads

• Change mode
• Log out

Use app×