If 1- m - n are real- - m- then the roots of the equation 1- m x 2-51- m x -2 l - m -0- areA- real and equalB- real and unequalC- no solutionD- None of the above

The correct option is A real and equalDiscriminant of the given equation is nbsp; D=25(l+m)^2+8(l m)^2 ⇒ (l m)^2 gt;0(∵ l≠ m), (l+m)^2≥0 ∴ D gt;0 hence ...

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Standard XII

Mathematics

Higher Order Equations

If 1, m , n a...

Question

If $l, m, n$ are real, $l \neq m$ , then the roots of the equation $(l - m) x^{2} - 5 (l + m) x - 2 (l - m) = 0$ , are

real and equal

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real and unequal

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no solution

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None of the above

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Solution

The correct option is A real and equal
Discriminant of the given equation is
$D = 25 (l + m)^{2} + 8 (l - m)^{2} \Rightarrow (l - m)^{2} > 0 (∵ l \neq m), (l + m)^{2} \geq 0 ∴ D > 0$
hence the roots are real and unequal

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Similar questions

Q. If

l, m, n

are real and

l \neq m

, the roots of the equation

(l - m) x^{2} - 5 (l + m) x - 2 (l - m) = 0

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Q. Objective Questions (MCQ)

In the equation

a x^{2} + b x + c = 0

, it is given that

D = (b^{2} - 4 a c) > 0

. Then, the roots of the equation are

(a) real and equal (b) real and unequal
(c) imaginary (d) none of these

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If l,m,n are real, l≠m, then the roots of the equation (l−m)x2−5(l+m)x−2(l−m)=0, are

The correct option is A real and equalDiscriminant of the given equation is D=25(l+m)2+8(l−m)2⇒(l−m)2>0(∵l≠m), (l+m)2≥0∴D>0 hence the roots are real and unequal

If $l, m, n$ are real, $l \neq m$ , then the roots of the equation $(l - m) x^{2} - 5 (l + m) x - 2 (l - m) = 0$ , are

The correct option is A real and equal
Discriminant of the given equation is
$D = 25 (l + m)^{2} + 8 (l - m)^{2} \Rightarrow (l - m)^{2} > 0 (∵ l \neq m), (l + m)^{2} \geq 0 ∴ D > 0$
hence the roots are real and unequal