Only two out of three are known

Algebra Level 2

$Q(x,y)= x^3 -3x^2y+p_1xy^2 +p_2 y^3$

If $x-y$ and $y-2x$ are two factors of the expression $Q(x,y)$ , then find the values of $p_1$ and $p_2$ .

p_1=\frac{11}{4},p_2=\frac {-3}{ 4}

p_1=\frac{-11}{4},p_2=\frac 3 4

p_1=\frac{11}{4},p_2=\frac 3 4

p_1=\frac{-11}{4},p_2=\frac{- 3}{ 4}

2 solutions

Devin Ky
Jul 21, 2015

By the factor theorem, Q (x,y) = 0 when x = y and y = 2x. Substituting and cancelling out x^3 (since x = 0 is a trivial solution) yields p1 + p2 = 2 and 4p1 + 8p2 = 5, which can be solved simultaneously to obtain p1 = 11/4 and p2 = -3/4.

Don't solve simultaneously, check for options which satisfy p1+p2=2!

Skanda Prasad - 3 years, 1 month ago

Atharva Chute
Mar 23, 2017

(x-y)(y-2x)(some factor) = given expression. Since coefficient of x^3 and x^2y is given. The unknown factor can be evaluated. And thus, p1 and p2.

Only two out of three are known

2 solutions

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