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  4. The number of integral values of b, for which the equation x2+bx-16=0 has integral roots, is

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Q. The number of integral values of $b$, for which the equation $ {{x}^{2}}+bx-16=0 $ has integral roots, is

KEAMKEAM 2011Complex Numbers and Quadratic Equations

Solution:

A quadratic equation $ {{x}^{2}}+bx-16=0 $ have integer roots, when it has following conditions. I. b must be even integer. II. its discriminant is a perfect square of an even number. So, $ D={{b}^{2}}+4.16={{b}^{2}}+64 $ Here, 0 and 6 only the even integers value of b, on which the discriminant of given quadratic equation have perfect square of an even number. So, the number of integral values of b is 2.