Question

For what values of k will the functon f(x)=kx^2-4x+k have no zeros

Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 have 2 zeros

Answer 1

if b^2 - 4ac < 0 ---> no real zeros
if b^2 - 4ac = 0 ---> one real zero
ifb^2 - 4ac > 0 ---> two real zeros

if will do the 2nd question.
a=4, b= 2k-3 , c = 1

b^2 - 4ac
= (2k-3)^2 - 4(4)(1)
= 4k^2 - 12k + 9 - 16
= 4k^2 - 12k - 7
= (k + 1)(4k - 7)

(k+1)(4k-7) > 0 for 2 real roots
k < -1 OR k > 7/4