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# polynomial

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Let a and b real numbers such that x^4+2x^3-4x^2+ax+b = (Q(x))^2 for some polynomial Q(x). What is the value of a + b?

Jan 7, 2021

#1
+112816
-1

$$(Q(x))^2=x^4+2x^3-4x^2+ax+b$$

Q(x) will have degree 2 and a leading coefficient of  +1 or -1

let

$$Q(x)=\pm(x^2+mx+n)\\ (Q(x))^2=?$$

do the multiplication and then equate the co-efficients.

etc

Jan 7, 2021