Let f x be a quadratic polynomial such that f – 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 , then its other root lies in

Question

Let f x be a quadratic polynomial such that f &#8211; 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 , then its other root lies in

Aicharya · Accepted Answer

Let f x = a x 2 + b x + c be a quadratic equation with roots &#945; , &#160; &#946; f 2 + f - 1 = 0 &#8658; 5 a + b + 2 c = 0 Also f 3 = 0 &#8658; 9 a + 3 b + c = 0 &#8658; a - 5 = b 13 = c 6 Product of roots &#945; &#946; = c a = - 6 5 We know &#945; = 3 &#8658; &#946; = - 2 5 &#8712; - 1 , 0

Let f x be a quadratic polynomial such that f – 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 ,…

Solution

Let f x be a quadratic polynomial such that f &#8211; 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 ,…

Solution

Let f x be a quadratic polynomial such that f – 1 + f 2 = 0 . If one of the roots of f x = 0 is 3 ,…