QJEEM19Mab90e: JEE Main 2019 Mathematics - Class 12 JEEM19Mab90e Solution: If lim x → 1 ⁡ x 2 − a x + b x − 1 = 5 , then a + b is equal to :

Question

Verified Solution • 2025–26 Session moderate

If

lim_{x \to 1} \frac{x^{2} - a x + b}{x - 1} = 5

, then a + b is equal to :

Accepted Answer

lim_{x \to 1} \frac{x^{2} - a x + b}{x - 1} = 5

\Rightarrow

(1)^{2} - a (1) + b = 0

\Rightarrow

1 - a + b = 0

\Rightarrow

a - b = 1 . . . . . . (1)

Now 'L' hospital rule

2x - a = 5

\Rightarrow

2 - a = 5 (

∵

x = 1)

\Rightarrow

a = - 3

By putting a = -3 in (1)

\Rightarrow

b = -4

∴

a + b = -7

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