If l-m-n are real- l- m- then the roots of the equation l-mx2-5l-mx-2l-m-0- are

Discriminant 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, the roots are real and uneq ...

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Standard XIII

Mathematics

Nature of Roots

If l,m,n are ...

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 unequal

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None of the above

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no solution

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real and equal

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Solution

The correct option is D 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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If $l, m, n$ are real, $l \neq m$ , then the roots by the equation: $(l - m) x^{2} - 5 (l + m) x - 2 (l - m) = 0$ are:

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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 D 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 D 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.