Question

If one of the zeros of the quadratic polynomial f(x)=14x²-42k²x-9 is negative find the value of k

Answer 1

     f (x) =  14 x²  -  42  k² x - 9
   root =   [ 42 k²  + -  √ (42² k⁴ + 504) ] / 28
           = 3 * [ 7 k² + - √(7² k⁴ + 14) ] / 14

  since k² is non negative,
       7 k²  <  √ (7 k⁴ + 14)
  so we will have one root negative and one root positive.
  This is true for any real  value of  k.

Answer 2

Answer:HEY MATE

Step-by-step explanation:

Comparing f(x) = 4x2 - 8kx - 9 with ax2+bx+c we get

a=4; b=-8k and c=-9.

Since one root is the negative of the other, let us assume that the roots are p an -p.

Sum of the roots, a+(-a)=-b/a= - (-8k) / 4

0=2k

k=0

HOPE THIS HELPED YOU........