LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
21 views
in Quadratic Equations by (54.3k points)
closed by
If α and β are the roots of the equation x2 - 2x + 4 = 0, then what is the value of α2 - β2?  
1. 12
2. 43
3. 567
4. None of these

1 Answer

0 votes
by (30.0k points)
selected by
 
Best answer
Correct Answer - Option 4 : None of these

Concept:

Consider a quadratic equation ax2 + bx + c = 0

Sum of roots  = \(\rm \frac{-b}{a}\) 

Products of roots = \(\rm \frac{c}{a}\)

(α + β)= α2 + β+ 2αβ

(α - β)= α2 + β2 - 2αβ

α2 - β2 = (α - β) (α + β)

Calculation:

Given: x2 - 2x + 4 = 0

Here a = 1, b = - 2,  c = 4

Let roots of the equation are α and β.

Sum of roots  = \(\rm \frac{-(-2)}{1}\) 

α + β = 2 

Products of roots = \(\rm \frac{4}{1}\) 

α β = 4    

α2 + β= (α + β)2  - 2αβ = (2)2 - 2(4) = 4 - 8 = - 4

(α - β)= α2 + β2 - 2αβ = - 4 - 2(4) = - 12

α - β = \(\rm 2i\sqrt{3}\)

α2 - β2 = \(\rm 4i\sqrt{3}\) 

The value of α2 - β2 is \(\rm 4i\sqrt{3}\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...