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
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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