An algebra problem by jazel libaton

Algebra Level 2

If 2 x 2 − 7 x − 4 = p ( x + 2 ) 2 + q ( x + 2 ) + r 2x^2-7x-4=p(x+2)^2+q(x+2)+r is an algebraic identity, find the values of p,q,and r.

p=3;q=-11;r=4 p=2;q=-15;r=18 p=3;q=-11;r=5 p=3;q=-11;r=6

Jazel Libaton by jazel libaton , 19, Philippines

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1 solution

Md Mehedi Hasan
Oct 31, 2017

here,

p ( x + 2 ) 2 + q ( x + 2 ) + r = p x 2 + 4 p x + 4 p + q x + 2 q + r = p x 2 + ( 4 p + q ) x + ( 4 p + 2 q + r ) p(x+2)^2+q(x+2)+r\\=px^2+4px+4p+qx+2q+r\\=px^2+(4p+q)x+(4p+2q+r)

comparing with 2 x 2 − 7 x − 4 2x^2-7x-4 we find

p = 2 4 p + q = − 7 4 p + 2 q + r = − 4 p=2\\4p+q=-7\\4p+2q+r=-4

Solving, p = 2 , q = − 15 , r = 18 p=\boxed2,\\ q=\boxed{-15},\\ r=\boxed{18}

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