Question

There are no results for If the roots of the equation, (a 2 +b 2 )x 2 -2(ac+bd)x+(c 2 +d 2 ) = 0 are equal the prove that ad = bc.

Answer 1

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• If roots are equal , then ∆ = 0

Given equation,

• (a²+b²)x² - 2(ac+bd)x + (c²+d²) = 0

Calculating the value of ∆

• ∆ = (2(ac+bd))² - 4(a²+b²)(c²+d²) = 0

• 4(ac)²+4(bd)²+8acbd -4(ac)² -4(ad)² -4(bc)² -4(bd)² = 0

• 8abcd - 4(ad)² -4(bc)² = 0

• -4(ad-bc)² = 0

• ad - bc = 0

• ad = bc

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