Find all the integral values of lsquo a lsquo for which the quadratic equation x ndash a x ndas...........

Mathematics (NDA) Quadratic Equations

Find all the integral values of ‘a ‘ for which the quadratic equation (x – a)(x – 10) + 1 = 0 has integral roots?

10,6

12,7

12,8

10,9

Here the equation is x² – (a + 10)x + 10a + 1 = 0. Since integral roots will always be rational it means D should be a perfect square

D=a²-20a+96

4=(a-10)² -D

If D is a perfect square it means we want difference of two perfect square as 4 which is possible

Only when (a-10)²=4 and D=0

(a-10)=±2

a=12,8

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