If the roots of the equation (a2 - bc)x2 + 2(b2 - ac)x + (c2 - ab) = 0 are equal

• Quant Quadratic

If the roots of the equation (a² - bc)x² + 2(b² - ac)x + (c² - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

1. a³ + b³ + c³ = 0
2. a³ + b³ + c³ = 3abc
3. a² + b² + c² = 0
4. a + b + c = abc

Answer

If Ax² + Bx + C = 0 has equal roots, then B² = 4AC. Using this, we have

(2(b² - ac))² = 4×(a² - bc)(c² - ab)

(b² - ac)² = (a² - bc)(c² - ab)

b⁴ + a²c² - 2ab²c = a²c² - a³b - bc³ + ab²c

b⁴ - 2ab²c = - a³b - bc³ + ab²c

b⁴ + a³b + bc³ = 2ab²c + ab²c

b (a³ + b³ + c³) = b(3abc)

a³ + b³ + c³ = 3abc

The correct option is B.