(x+2)(x+a)=x^2+5x+b

In the equation above, a and b are positive integers. If the equation is true for all values of x, what is the value of b?

The answer is 6, but I need to know how to work the problem.

given (x+2)(x+a)=x^2+5x+b where a and b are positive integers

first expand (x+2)(x+a)=x^2+2x+ax+2a

factorize as x^2+(2+a)x+2a

from the general quadratic expression mx^2+kx+C where m,k are variable and c is a constant

compare m=1 , k=2+a and C=2a

now compare coefficients of expression in the right side of given question

i.e., 5=2+a and b=2a

so a=5-2=3

hence b=2*3=6

thank you

Thank you, but why do you need to expand the formula that way?

in quadratic expressions of power 2 series we expand so that we can express it in general quadratic equation form or standard form so as we can compare variables and coefficient

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