Question

\exists x \forall y \left( 2y^2 + y \right) x^2 - \left( 8y^2 + 10y \right) x - 24\left( y^2 - y \right) = 0

Name: ∃x ∀y ( 2y^2 + y ) x^2 - ( 8y^2 + 10y ) x - 24( y^2 - y ) = 0
Uploaded: 2020-08-02T15:38:28-08:00
Duration: 6 min 30 s
Channel: Sinisa Stura
Description: ∃x ∀y ( 2y^2 + y ) x^2 - ( 8y^2 + 10y ) x - 24( y^2 - y ) = 0

          \exists x \forall y \left( 2y^2 + y \right) x^2 - \left( 8y^2 + 10y \right) x - 24\left( y^2 - y \right) = 0

Added by Gloria R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sinisa Stura

08/02/2020

Step 1

We want to find if there exists an $x$ such that for all $y$, $P(x,y) = 0$. If $y=0$, then $P(x,0) = 0$. If $y=1$, then $P(x,1) = 3x^2 - 18x = 3x(x-6) = 0$, so $x=0$ or $x=6$. If $y=2$, then $P(x,2) = 10x^2 - 44x - 48 = 0$, which gives $5x^2 - 22x - 24 = 0$. Show more…

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