maths c1 AS level

given that the equation 4x^2-kx+k-3=0 where k is a constant, has real roots ,show that k^2-16k+48>=0
which i got the answer to. Later on it asks the set of possible values of k which was k>=12 or k<=4. After these two questions it asks for the smallest value of k for which the roots are equal and solve the equation when k takes this value.
Would really appreciate the help since I don't have a good maths teacher at all! Thank you :smile:

(edited 6 years ago)

Reply 1

Ladkus

Since the equation has real roots you know that the decriminant of the quadratic is more than or equal to 0 so b²-4ac>=0 where a is 4x², b is -k and c is k-3

Reply 2

TJHEY12

Original post by Ladkus

Since the equation has real roots you know that the decriminant of the quadratic is more than or equal to 0 so b²-4ac>=0 where a is 4x², b is -k and c is k-3

thank you so much that helped a lot! managed to figure it out thanks to you!