Question

If the roots of 2x2 - 6x + k = 0 are real and equal, find k.

Answer 1

Answer:

Step-by-step explanation:

2x2+6x+k=2(x−α)(x−β)=2x2−2(α+β)+2αβ

α+β=−3

αβ=k/2

αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=(α+β)2αβ−2=18k−2

For k<0 this increases as k→−∞. αβ+βαnever reaches its least upper bound aka supremum of negative two.

Answer 2

Hi Mate!!!

For real roots Descrimnant (D) must be greater then 0

D = √( 36- 8k)

√ ( 36-8k ) >0

Squaring both sides

36 > 8k

k < 36/8

k < or equal to9/2