WMA11 Jan 2023

• WMA11/01 (Edexcel) IAL P1 January 2023, Q4 (Quadratics:​​ Discriminant)

Given that the equation​​ 

kx2+6kx+5=0  where k is a non zero constant

has no real roots, find the range of possible values for k.

(4)

SOLUTION

Since, the questions says that the function has no real roots, so the discriminant must be less than 0.​​ 

The given quadratic equation is​​ kx2+6kx+5=0, where​​ a=k, b =6k, & c=5.

b2-4ac<0

6k2-4k5<0

36k2-20k<0

9k2-5k<0

9k2-5k=0

k9k-5=0

k=0   ,  k=59

The yellow portion of line represents the value of k as the inequality sign in was ‘’less than’’.​​ 

Hence, the range of k is​​ 

0<k<59