CAT 2024 - Slot 1 Quant Question 3
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CAT 2024 Slot 1 - Quant
When given more than one equations, stating the fact that there is a common root,
We need to equate the two equations to get discernible values for x
Here, we are given three equations with the values of m, n
x2 + mx + 9 = x2 + (m + n)x + 35
mx + 9 = mx + nx + 35
nx = – 26
Similarly, we can do it for the other equation as well,
x2 + nx + 17 = x2 + (m + n)x + 35
mx = – 18
Substituting the value of either mx or nx in the original equations, we get
x2 – 18 + 9 = 0
x2 = 9
x = ± 3
Since we are given that the root is negative, x = – 3
n = – (26/– 3)
m = – (18/– 3)
3n = 26
2m = 12
2m + 3n = 38