What is the value of n such that the expression x^2 + 11x + n is a perfect

Chesley

Chesley

Answered question

2021-10-01

What is the value of n such that the expression x2+11x+n is a perfect square trinomial?

A. 11

B. 25

C. 30.25

D. 36

Answer & Explanation

unessodopunsep

unessodopunsep

Skilled2021-10-02Added 105 answers

Given:
x2+11x+n
We need to determine the value such that the expression is a perfect-square trinomial.
A perfect-square polynomial is of the form (a±b)2=(a±b)(a±b)=a2±2ab+b2
Let us write the given expression in the form a2±2ab+b2
x2+2x112+n
Comparing the previous expression to a2±2ab+b2, we note that n needs to be equal to b2 and b needs to be equal to 112
n=b2
b=112
Substitute b by in the equation n=b2
n=b2=(112)2=112112112=1214=30.25
Result: 30.25

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