First slide

Theory of equations

Question

The integral values of $a$ for which the quadratic equation
(x – a) (x – 10) + 1 = 0 has integeral roots are

Moderate

A

– 1, 3
B

2, 3
C

12, 8
D

– 8, – 12

Solution

If x is an integer and
$(x - a) (x - 10) = - 1$
$\Rightarrow x - 10 = 1 and x - a = - 1 or x - 10 = - 1 and$
$x - a = 1$
$\Rightarrow x = 11 and a = x + 1 = 12 or x = 9 and a =$
$x - 1 = 8$

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