Question

If x = 5 is a root of both the equations x² + mx – 15 = 0 and 2x² – 7x + n = 0, then find the value of mn + 2m – n.

Answer 1

Equation (1)

x² + mx − 15 = 0

Substitute x = 5:

25 + 5m − 15 = 0

10 + 5m = 0

5m = −10

⇒ m = −2

Equation (2)

2x² − 7x + n = 0

Substitute x = 5:

2(25) − 35 + n = 0

50 − 35 + n = 0

15 + n = 0

⇒ n = −15

Substitute m = −2, n = −15:

mn + 2m − n

= (−2) (−15) + 2(−2) − (−15)

= 30 − 4 + 15

= 41