The value of b for the quadratic equation x2 bx 5 = 0 to have two real number solutions is -5.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
The quadratic equation has two real number solutions when the value of the following equation is positive.
[tex]b^2-4ac[/tex]
The quadratic equation given in the problem is,
[tex]x^2 +bx+ 5 = 0[/tex]
The value of b has to be found out such that the equation have two real number solutions. For this equation,
[tex]a=1\\c=5[/tex]
Put this value in the above equation as,
[tex]b^2-4\times1\times5\\b^2-20[/tex]
The value of the above expression to be positive, the value of b should be at least 5 or -5.
[tex](-5)^2-20\\25-20\\5[/tex]
Thus, the value of b for the quadratic equation x2 bx 5 = 0 to have two real number solutions is -5.
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