If the quadratic equation (a2-b2) x2+(b2-c2) x+ (c2-a2)=0 has equal roots, then which of the following is true?

Question

If the quadratic equation (a2-b2) x2+(b2-c2) x+ (c2-a2)=0 has equal roots, then which of the following is true? (A) b2+c2=a2 (B) b2+c2=2 a2 (C) b2-c2=2 d2 (D) d2=b2+2 c2

Tardigrade Admin · Accepted Answer

Observe the coefficient of each term and guess one root

Q. If the quadratic equation $(a^{2} - b^{2}) x^{2} + (b^{2} - c^{2}) x +$ $(c^{2} - a^{2}) = 0$ has equal roots, then which of the following is true?

$b^{2} + c^{2} = a^{2}$

$b^{2} + c^{2} = 2 a^{2}$

$b^{2} - c^{2} = 2 d^{2}$

$d^{2} = b^{2} + 2 c^{2}$

Observe the coefficient of each term and guess one root

Q. If the quadratic equation (a2−b2)x2+(b2−c2)x+ (c2−a2)=0 has equal roots, then which of the following is true?

b2+c2=a2

b2+c2=2a2

b2−c2=2d2

d2=b2+2c2

Observe the coefficient of each term and guess one root

Q. If the quadratic equation $(a^{2} - b^{2}) x^{2} + (b^{2} - c^{2}) x +$ $(c^{2} - a^{2}) = 0$ has equal roots, then which of the following is true?

$b^{2} + c^{2} = a^{2}$

$b^{2} + c^{2} = 2 a^{2}$

$b^{2} - c^{2} = 2 d^{2}$

$d^{2} = b^{2} + 2 c^{2}$