Question

If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.

Answer 1

it's 12 and -12

Step-by-step explanation:

i didnt know there was two answers, and i was so confused

Answer 2

±12 (two answers)

Step-by-step explanation:

Suppose one root is a. Then the other root will be -3a. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:

(a)(-3a) = -27/4

a² = -27/(4·(-3)) = 9/4

a = ±√(9/4) = ±3/2

Then the other root is

-3a = -3(±3/2) = ±9/2 . . . . . . the roots will have opposite signs

We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...

-(a + (-3a)) = b/4

2a = b/4

b = 8a = 8·(±3/2)

b = ±12

_____

Check

For b = 12, the equation factors as ...

4x² +12x -27 = (2x -3)(2x +9) = 0

It has roots -9/2 and +3/2, the ratio of which is -3.

For b = -12, the equation factors as ...

4x² -12x -27 = (2x +3)(2x -9) = 0

It has roots 9/2 and -3/2, the ratio of which is -3.