BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 10, Problem 7CA

To determine

To find the number of zeros.

Expert Solution & Answer

Answer to Problem 7CA

$No zerosOne zeroTwo zerosf(x)=3x2+4x+2f(x)=−6x2−5f(x)=4x2−8x+4f(x)=7x2f(x)=−x2+2xf(x)=x2−3x−21$

Explanation of Solution

Given information: $f(x)=3x2+4x+2$ , $f(x)=4x2−8x+4$ , $f(x)=7x2$ , $f(x)=−x2+2x$ , $f(x)=x2−3x−21$ and $f(x)=−6x2−5$

Formula Used: $D=b2−4ac$

Calculation:

Discriminant be used to confirm the number of real solutions of a quadratic equation because discriminant method is much easier and shorter than completing the square method.

We can easily calculate discriminant by $D = b2−4ac$ and can know how many real numbers equation has.

If $D$ equal to negative then $x$ has no real solution.
If $D$ equal to 0 then $x$ has 1 real solution.
If $D$ equal to positive then $x$ has 2 real solution.

(1)

$f(x)=3x2+4x+2$

As, $D = b2−4ac$

Now, $a=3$ , $b=4$ and $c=2$

$D = 42−4×3×2$

So,

$D = 16−24$

Hence,

$D =−8$

$D$ is equal to negative then $x$ has no real solution.

(2)

$f(x)=4x2−8x+4$

As, $D = b2−4ac$

Now, $a=4$ , $b=−8$ and $c=4$

$D = (−8)2−4×4×4$

So,

$D = 64−64$

Hence,

$D =0$

$D$ is equal to 0 then $x$ has 1 real solution.

(3)

$f(x)=7x2$

As, $D = b2−4ac$

Now, $a=7$ , $b=0$ and $c=0$

$D = (0)2−4×7×0$

So,

$D = 0−0$

Hence,

$D =0$

$D$ is equal to 0 then $x$ has 1 real solution.

(4)

$f(x)=−x2+2x$

As, $D = b2−4ac$

Now, $a=−1$ , $b=2$ and $c=0$

$D = (2)2−4×(−1)×0$

So,

$D = 4−0$

Hence,

$D =4$

$D$ is equal to positive then $x$ has 2 real solution.

(5)

$f(x)=x2−3x−21$

As, $D = b2−4ac$

Now, $a=1$ , $b=−3$ and $c=−21$

$D = (−3)2−4×1×(−21)$

So,

$D = 9+84$

Hence,

$D =93$

$D$ is equal to positive then $x$ has 2 real solution.

(6)

$f(x)=−6x2−5$

As, $D = b2−4ac$

Now, $a=−6$ , $b=0$ and $c=−5$

$D = (0)2−4×(−6)×(−5)$

So,

$D = 0−120$

Hence,

$D =−120$

$D$ is equal to negative then $x$ has no real solution.

Hence Solution,

$No zerosOne zeroTwo zerosf(x)=3x2+4x+2f(x)=−6x2−5f(x)=4x2−8x+4f(x)=7x2f(x)=−x2+2xf(x)=x2−3x−21$

Chapter 10, Problem 6CA

Chapter 10, Problem 8CA

Chapter 10 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 1Q Ch. 10.3 - Prob. 2Q Ch. 10.3 - Prob. 3Q Ch. 10.3 - Prob. 4Q Ch. 10.3 - Prob. 5Q Ch. 10.3 - Prob. 6Q Ch. 10.3 - Prob. 7Q Ch. 10.3 - Prob. 8Q Ch. 10.3 - Prob. 9Q Ch. 10.3 - Prob. 10Q Ch. 10.3 - Prob. 11Q Ch. 10.3 - Prob. 12Q Ch. 10.3 - Prob. 13Q Ch. 10.3 - Prob. 14Q Ch. 10.3 - Prob. 15Q Ch. 10.3 - Prob. 16Q Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Prob. 34E Ch. 10.4 - Prob. 35E Ch. 10.4 - Prob. 36E Ch. 10.4 - Prob. 37E Ch. 10.4 - Prob. 38E Ch. 10.4 - Prob. 39E Ch. 10.4 - Prob. 40E Ch. 10.4 - Prob. 41E Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Prob. 21E Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Prob. 27E Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10.5 - Prob. 33E Ch. 10.5 - Prob. 34E Ch. 10.5 - Prob. 35E Ch. 10.5 - Prob. 36E Ch. 10 - Prob. 1CR Ch. 10 - Prob. 2CR Ch. 10 - Prob. 3CR Ch. 10 - Prob. 4CR Ch. 10 - Prob. 5CR Ch. 10 - Prob. 6CR Ch. 10 - Prob. 7CR Ch. 10 - Prob. 8CR Ch. 10 - Prob. 9CR Ch. 10 - Prob. 10CR Ch. 10 - Prob. 11CR Ch. 10 - Prob. 12CR Ch. 10 - Prob. 13CR Ch. 10 - Prob. 14CR Ch. 10 - Prob. 15CR Ch. 10 - Prob. 16CR Ch. 10 - Prob. 17CR Ch. 10 - Prob. 18CR Ch. 10 - Prob. 19CR Ch. 10 - Prob. 20CR Ch. 10 - Prob. 1CT Ch. 10 - Prob. 2CT Ch. 10 - Prob. 3CT Ch. 10 - Prob. 4CT Ch. 10 - Prob. 5CT Ch. 10 - Prob. 6CT Ch. 10 - Prob. 7CT Ch. 10 - Prob. 8CT Ch. 10 - Prob. 9CT Ch. 10 - Prob. 10CT Ch. 10 - Prob. 11CT Ch. 10 - Prob. 12CT Ch. 10 - Prob. 13CT Ch. 10 - Prob. 1CA Ch. 10 - Prob. 2CA Ch. 10 - Prob. 3CA Ch. 10 - Prob. 4CA Ch. 10 - Prob. 5CA Ch. 10 - Prob. 6CA Ch. 10 - Prob. 7CA Ch. 10 - Prob. 8CA Ch. 10 - Prob. 9CA

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