Find the minimum value of x^2 + 7x + 14.

Question

Find the minimum value of  x^2 + 7x + 14 .

A. 14
B. -7
C. 0
D. 7
E. 1.75

Bunuel · Accepted Answer

x^2 + 7x + 14=x^2+2*3.5x + 3.5^2 + 1.75=(x + 3.5)^2 + 1.75 .

The least value of (x + 3.5)^2 is obviously 0 (for x = -3.5), thus the least value of the whole expression is 1.75.

Answer: E.

sukoon9334 · Answer

How do we find roots of such questions?

Score-Quest · Answer

Although finding the roots of this expression isn't necessary to answer the question, as shown by Bunuel, if you are still interested, you can determine them using the below formula:
 x= \frac{−b±\sqrt{b^2-4ac}}{2a}  
where a=coefficient of x^2, b=coefficient of x and c=constant

So, for this expression, the roots will be:
​ x= \frac{−7±\sqrt{49-4*1*14}}{2*1} = \frac{−7±\sqrt{-7}}{2}  
Since the roots contain square root of a negative number, the roots will be complex numbers as follows:
 x=\frac{-7}{2}+\frac{\sqrt{7}}{2}i  and  x=\frac{-7}{2}-\frac{\sqrt{7}}{2}i

Hope this helps!
​

HSWorNothing · Answer

Using differential equations to find the maxima/minima is a huge time saver on GMAT (if you can get comfortable with it). Here's a great link/resource. It is super simple in my opinion.

https://www.mathsisfun.com/calculus/maxima-minima.html

treeetravel · Answer

Calcuakte the differential of equation w.r.t x, which comes out 2x+7. Equate this with zero and x = -7/2. Put this value in the orginal equation to calculate minimum value that comes out 1.75.

For equation with no complex roots, maxima/minma concept of differential equation is used.

Posted from my mobile device

samarpan.g28 · Answer

Use the formula x=-(b/2a) to calculate maxima or minima given coefficient a>0 or <0.

Kinshook · Answer

Find the minimum value of  x^2 + 7x + 14 .

x^2 + 7x + 14= (x+3.5)^2 +1.75/m].

Minimum value is at x =-3.5 e.g. 1.75

IMO E

SwapnilBangera · Answer

Use the vertex formula for a quadratic
A quadratic in the form:

ax^2+bx+c

has its minimum or maximum (depending on which side the parabola opens) at:

x=−b/2a

For our expression:

a=1
b=7

x=−7/2

Plug back to find the minimum value
Substitute x=−7/2 into the expression which gives

7/4 = 1.75
​

Sabuj40040 · Answer

Let, y=x2+7x+14

dy/dx=d/dx(x2+7x+14)

=2x+7

Now, 2x+7=0

Therefore, x=-7/2

Putting x=-7/2 into y= x2+7x+14

We get, y=(-7/2)2+7(-7/2)+14

=7/4=1.75

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Find the minimum value of x^2 + 7x + 14.

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Find the minimum value of x^2 + 7x + 14.

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