Question

if l,m and n are real and $l \neq m$ , then the roots of the equation
[tex](l-m) x^{2} - 5(l+m)x - 2(l-m) + 0
[/tex] , are
a) real and equal
b) complex
c) real and unequal
d) none of this

Answer 1

(l - m)x² -5( l + m)x -2(l - m) = 0
where l ≠ m

find Discriminant = b² - 4ac
= {5(l + m)}² + 8( l - m)²
= 25l² + 25m² + 50ml - 8l² - 8m² -16ml
= 17l² + 17m² + 34ml
=17{ l² + m² + 2ml }
= 17( l + m)² > 0
hence, D> 0 so, roots are real and unequal . option (C) is correct .

Answer 2

Hey hi !

(l - m)x² -5( l + m)x -2(l - m) = 0

a = l  - m
b =  - 5 ( l+m)
c = -2(l-m)


Here 
l  ≠ m 

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In order to find the nature of roots , we have to find the discriminant :-

b² - 4ac is the discriminant :-



 so,
= [5(l + m)]²   - 4 × (l-m) × - 2 (l-m)
 =  [5(l + m)]² + 8( l - m)² 
= 25l² + 25m² + 50ml - 8l² - 8m² -16ml
= 17l² + 17m² + 34ml
=17[ l² + m² + 2ml ]
= 17( l + m)²


 17( l + m)² > 0

When b²- 4ac > 0 , the nature of roots is => 
Real and unequal

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IF b²- 4ac = 0 , the roots would have been equal roots
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If b²- 4ac < 0 , then there would be no real roots !