Question

What value for c will make the expression a perfect square trinomial?

x2 – 7x + c

negative StartFraction 49 Over 4 EndFraction
negative seven-halves
seven-halves

Answer 1

For x^2 − 7x + c to be a perfect square, write it as (x − a)^2 = x^2 − 2ax + a^2. So −7 = −2a ⇒ a = 7/2. Then c = a^2 = (7/2)^2 = 49/4. The trinomial is (x − 7/2)^2.

(Neither −49/4, −7/2, nor 7/2 from your listed choices equals 49/4; 7/2 is a, not c.)