Let a , b , c be in arithmetic progression. Let the centroid of the triangle with vertices a , c , 2 , b and a , b be 10 3 , 7 3 . If α , β are the roots of the equation a x 2 + b x + 1 = 0 , then the value of α 2 + β 2 - α β is:

Question

Let a , b , c be in arithmetic progression. Let the centroid of the triangle with vertices a , c , 2 , b and a , b be 10 3 , 7 3 . If &#945; , &#946; are the roots of the equation a x 2 + b x + 1 = 0 , then the value of &#945; 2 + &#946; 2 - &#945; &#946; is:

Aicharya · Accepted Answer

a + 2 + a 3 = 10 3 a = 4 and c + b + b 3 = 7 3 c + 2 b = 7 also 2 b = a + c 2 b - a + 2 b = 7 b = 11 4 now 4 x 2 + 11 4 x + 1 = 0 &#945; 2 + &#946; 2 - &#945; &#946; = &#945; + &#946; 2 - 3 &#945; &#946; = - 11 16 2 - 3 1 4 = 121 256 - 3 4 = - 71 256

Let a , b , c be in arithmetic progression. Let the centroid of the triangle with vertices a , c , 2 , b and…

Solution