Question

The integral values of a for which the quadratic equation (x-a)(x-49)+1=0 has integral roots is

Answer 1

Answer:

Given :quadratic equation (x-a)(x-49)+1=0

 To find :  the value of m so that quadratic equation has two equal roots.

=> mx(x-7)+49=0.....(1)

=> mx2 - 7mx +49 =0

it is a quadratic equation where a = m , b =-7m , c = 49

 For equal roots D =0

D = b2 - 4ac =0    => (-7m)2 - 4 (m)(49) =0     => 49m2 - 4 m(49) =0     => m2 -4m =0      => m (m-4) =0       => m =0 and m =4   Since m=0 is invalid here as by putting the value in the eq (1)   => 0 + 49 = is not equal to 0

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