Question

Let f(x) = ax2 + bx + c, where a,b and c are certain constants and a≠0. It is known that  f (5) = -3f(2) and that 3 is a root of f(x) = 0.  21. What is the other root of f(x) = 0? 

Answer 1

1. x = k is a root of the equation P(x) = 0. 2. ... The quadratic polynomial equation Q(x) =ax2 + bx + c = 0 has two roots that may be: ... 0. 1. 3. Mathematics Learning Centre, University of Sydney. 2. 1. Let Q(x) = x2 − 4x + 3. .... 5. 1.2.2 The Remainder Theorem. If the polynomial f(x) is divided by (x − a) then the remainder is f(a).21 2. 61 4. 41 5. 81 3. 781 3. 01 3. If the roots of the equation x3 - ax2 + bx - c = 0 are three consecutive ... 5 and 6: Let f (x) = ax2 + bx + c, where a, b and c are certain constants and a ^ 0. It is known that f (5) = - 3 f(2) and that 3 is a root of f(x) = 0. 5. What is the other root of f(x) = 0? 1.-7 4. 6 2.-4 5. annot be determined 3. 2 

Answer 2

Answer:

Step-by-step explanation:

: ax^2+bx+c=k [x^2 -(α+β)x+αβ]    

              Equating co-efficient of x^2, x & constant terms on both sides, we get

                               a = k                      . . . . . . . . . . . . . .(1)

                               b = -k(α+β)    . . . . . . . . . . . . . .(2)

                               c = kαβ                 . . . . . . . . . . . . . .(3)

               Putting k=a in (2) & (3) we get

                               b= -a(α+β)  &  c = aαβ

                               ∴ α+β = - b/a   &  αβ = c/a  

               Thus if α, β are zeroes of the quadratic polynomial ax^2+bx+c,   a≠0 then

               Sum of zeroes = α+β = -b/a  = - (coefficient of x)/(coefficient of x^2 )