218k views
4 votes
2x2 + 7x = 3

x = 0.60 and x = −2.60
x = −0.60 and x = 2.60
x = 0.39 and x = −3.89
x = −0.39 and x = 3.89

1 Answer

2 votes

Answer:

(c) x = 0.39 and x = -3.89

Explanation:

You want the solutions to the quadratic equation ...

2x² +7x = 3.

Root relations

The roots of the equation ...

x² +bx +c = 0

have a sum of -b and a product of c.

Subtracting 3 and dividing the equation by 2, we have ...

2x² +7x -3 = 0 . . . . . . . . subtract 3

x² +3.5x -1.5 = 0 . . . . . . divide by 2

This tells us the sum of the roots is -3.5.

Answer choice C has that sum: x = 0.39, x = -3.89.

__

Additional comment

The sums of the answer choices are ...

0.60 -2.60 = -2.00

-0.60 +2.60 = 2.00

0.39 -3.89 = -3.50

-0.39 +3.89 = 3.50

Sometimes, checking the offered choices is the simplest way to find the answer.

Here, checking the sum gives the best discriminator of right from wrong. The products are all near -1.5, so that is less helpful.

We can see the relation by considering the factored form:

(x -p)(x -q) = x² -(p+q)x +pq . . . . . . where p and q are the roots

<95141404393>

2x2 + 7x = 3 x = 0.60 and x = −2.60 x = −0.60 and x = 2.60 x = 0.39 and x = −3.89 x-example-1
User StrayCatDBA
by
8.4k points