Question

Ifx^2– px + 12 = (x – 3)(x – a) is an identity, then the values of a and p are respectively
(a) a = 4, p = 7 (b) a = 7, p = 4 (c) a = 4, p =-7 (d) a=-4, p = 7​

Answer 1

Answer:

(a) p = 7 and a = 4

Step-by-step explanation:

x² – px + 12 = (x – 3) (x – a)

If p = 7 then

∴ x² – 7x + 12 = (x – 3) (x – a)

∴ x² – 4x – 3x + 12 = (x – 3) (x – a)   ( splitting –7 = –4  and –3 )

∴ x ( x – 4) – 3 (x – 4) = (x – 3) (x – a)

∴ ( x – 3) ( x – 4)   = (x – 3) (x – a)

hence,   p = 7 and a = 4

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