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Standard X

Mathematics

Quadratic Formula

If tan A, t...

Question

If $tan A, tan B$ are the roots of the quadratic $a b x^{2} - c^{2} x + a b = 0$ , where $a, b, c$ are the sides of a triangle, then prove
$tan A + tan B = \frac{c^{2}}{a b}$

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Solution

$a b x^{2} - c^{2} x + a b$
$tan A = α tan B = β$
$α + β = tan A + tan B = \frac{c^{2}}{a b}$

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If tanA,tanB are the roots of the quadratic ab x2−c2x+ab=0, where a,b,c are the sides of a triangle, then provetanA+tanB=c2ab

abx2−c2x+abtanA=αtanB=βα+β=tanA+tanB=c2ab

If $tan A, tan B$ are the roots of the quadratic $a b x^{2} - c^{2} x + a b = 0$ , where $a, b, c$ are the sides of a triangle, then prove
$tan A + tan B = \frac{c^{2}}{a b}$

$a b x^{2} - c^{2} x + a b$
$tan A = α tan B = β$
$α + β = tan A + tan B = \frac{c^{2}}{a b}$