Let non-zero, non-collinear vectors x , y satisfy ( a α 2 + b α + c ) x + ( a β 2 + b β + c ) y + ( a γ 2 + bγ + c ) ( x × y ) = 0 , where a , b , c ∈ R . Then a + b + c is

Question

Let non-zero, non-collinear vectors x , y ​ satisfy ( a α 2 + b α + c ) x + ( a β 2 + b β + c ) y ​ + ( a γ 2 + bγ + c ) ( x × y ​ ) = 0 , where a , b , c ∈ R . Then a + b + c is

TestHub · Accepted Answer

x , y ​ & x × y ​ are linearly independent ​ a α 2 + b α + c = 0 ​ a β 2 + b β + c = 0 ​ a γ 2 + bγ + c = 0 ​ ⇒ q u a d r a t i c a x 2 + b x + c = 0 has three roots α , β and γ ​ ⇒ a x 2 + b x + c = 0 is an identity ​ ⇒ a = b = c = 0 ​

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