Question

if one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k

Answer 1

Let f(x)=(k-2)x²-2x-(k+5).
Since 4 is a zero of f(x), BY FACTOR THEOREM,
f(4)=0
Therefore,
⇒(k-2)(4)²-(2*4)-(k+5)=0
⇒16k-32-8-k-5=0
⇒15k--45=0
⇒15k=45
⇒k=45/15
Therefore, k=3.






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Answer 2

4  is a root / zero  of    polynomial
         P(x)  =   (k-2) x²  - 2 x  - (k+5)

    =>  P(4) = 0
    =>  (k - 2) 4²  - 2 * 4 - (k+5)  = 0
    =>  15 k - 45 = 0   

              =>  k = 3