GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Select all the values of x which make the following true:
[#permalink]
30 May 2022, 03:44
30 May 2022, 03:44
Expert Reply
00:00
Question Stats:
53% (01:42) correct
46% (02:00) wrong based on 32 sessions
Hide Show timer Statistics
Select all the values of x which make the following true:\( 2x^4 = 7x^3 + 4x^2 \).
Indicate all that apply
(A) 0
(B) –1/2
(C) -1
(D) 2
(E) 4
Indicate all that apply
(A) 0
(B) –1/2
(C) -1
(D) 2
(E) 4
Re: Select all the values of x which make the following true:
[#permalink]
23 Jun 2022, 13:55
23 Jun 2022, 13:55
Expert Reply
1
Bookmarks
Strategy: There are two possible approaches here. We can test each answer choice by plugging it into the given equation to see if it satisfies that equation.
Since testing answer choice B (-1/2) looks like a pain, I'm going to solve the given equation for x.
Given: \( 2x^4 = 7x^3 + 4x^2\)
Since there appears to be a quadratic equation hiding in this equation, let's first set it equal to zero: \( 2x^4 - 7x^3 - 4x^2 = 0\)
Factor out \(x^2\) to get: \( x^2(2x^2 - 7x - 4) = 0\)
Since the first term of the quadratic equation inside the brackets is \(2x^2\), we know that the expression will factor into something that looks like this: \( x^2(2x ± ?)(x ± ?) = 0\)
Notice that the last two remaining terms must multiply to get \(-4\), so we need only test a few pairs of values until we got something that expands to get \(2x^2 - 7x - 4 = 0\)
Eventually we'll get: \( x^2(2x + 1)(x - 4) = 0\)
So it could be the case that \(x^2 = 0\), which means \(x = 0\)
Or it could be the case that \(2x+1 = 0\), which means \(x = -1/2\)
Or it could be the case that \(x - 4 = 0\), which means \(x = 4\)
Answer: A, B and E
Since testing answer choice B (-1/2) looks like a pain, I'm going to solve the given equation for x.
Given: \( 2x^4 = 7x^3 + 4x^2\)
Since there appears to be a quadratic equation hiding in this equation, let's first set it equal to zero: \( 2x^4 - 7x^3 - 4x^2 = 0\)
Factor out \(x^2\) to get: \( x^2(2x^2 - 7x - 4) = 0\)
Since the first term of the quadratic equation inside the brackets is \(2x^2\), we know that the expression will factor into something that looks like this: \( x^2(2x ± ?)(x ± ?) = 0\)
Notice that the last two remaining terms must multiply to get \(-4\), so we need only test a few pairs of values until we got something that expands to get \(2x^2 - 7x - 4 = 0\)
Eventually we'll get: \( x^2(2x + 1)(x - 4) = 0\)
So it could be the case that \(x^2 = 0\), which means \(x = 0\)
Or it could be the case that \(2x+1 = 0\), which means \(x = -1/2\)
Or it could be the case that \(x - 4 = 0\), which means \(x = 4\)
Answer: A, B and E
Re: Select all the values of x which make the following true:
[#permalink]
24 Jul 2022, 22:43
24 Jul 2022, 22:43
Quote:
Notice that the last two remaining terms must multiply to get −4−4, so we need only test a few pairs of values until we got something that expands to get 2x2−7x−4=02x2−7x−4=0
Eventually we'll get: x2(2x+1)(x−4)=0
Eventually we'll get: x2(2x+1)(x−4)=0
Sir, please explain the thought process behind this
