One of the solutions to the equation 5x^2+bx+12=0 is −4/5. Find the value of b.

Question

help please! thank you :)

Answer 1

Okay, so we have the equation 5x² +bx+12 = 0. One of the solutions to this equation is x = -4/5.

If we know the value of x, then we can easily solve for b.

First, try substituting x in this equation for -4/5. Every time you see an x, replace it with (-4/5).

(-4/5)² + b(-4/5) + 12 = 0. We don't need a calculator to do this.

Now, we know that a number (n) squared means you multiply it by itself once. n² = n x n = (n)(n).

So, (-4/5)² = (-4/5)(-4/5). If we multiply a negative by a negative we get a positive, so we can also write this as (4/5)(4/5).

To start solving for b, we want to get be to one side and all the numbers to the opposite side so we can get b = ____.

First, we should start with any addition or subtraction we see. Let's look at the +12. We want to bring that from the left side to the right side of the equation. We do that by doing the opposite operation to both sides.

The opposite of addition is subtraction.

(4/5)(4/5) + b(-4/5) +12 = 0

-12 -12

__________________________

(4/5)(4/5) + b(-4/5) = -12 Now, we can also subtract (4/5)(4/5) from both sides.

-(4/5)(4/5) -(4/5)(4/5)

__________________________

b(-4/5)= -12 -(4/5)(4/5) What can we do to get b by itself? We do the opposite operation. Since b

is multiplied by (-4/5) now we need to divide it by (-4/5) to get rid of (-4/5) on the left and move it to the right. Another way to divide fractions is to multiply by the reciprocal (multiply by the fraction flipped upside down. For example, if you 4 divided by 1/2 it is the same as 4 multiplied by 2/1. The reciprocal of (-4/5) is (-5/4), so we need to multiply both sides of the equation by (-5/4).

b(-4/5)x(-5/4) =(-5/4) x (-12 -(4/5)(4/5))

b = (-5/4) x (-12 -(4/5)(4/5)) Now we solve for b, multiply (-5/4) by 12 and (-5/4) by -(4/5)(4/5).

b = (-5/4) x -12 - (-5/4) (4/5) (4/5). First, -5/4 x 4/5 =-20/20 =-1.

b = (-5/4)(-12)-(-1(4/5). Next, -1 x 4/5 = -4/5. If we have - -4/5, this means we add 4/5. Subtracting a negative means we add.

b = (-5/4)(-12) + 4/5 Then, we need to multiply (-5/4) by -12. We can just multiply right across the top and do -5 times -12 then divide the answer by 4. (-5)(-12) = 60. 60/4 = 15.

b = 15 + 4/5

If we want to turn this into a decimal, we know 1/5 = .2. So, 4(1/5) = 4(.2) = .8.

b= 15+ .8

b= 15.8

Answer 2

When roots are given to get the quadratic equation :

For a quadratic equation ax²+bx+c = 0, the sum of its roots = –b/a and the product of its roots = c/a

let the roots be 'm' and 'n'

Given one root m = - 4/5

5x^2 + bx + 12 = 0

the sum of its roots = –b/a

m + n = - b/a

-4/5 + n = -b/5

-4 + 5n = -b

5n= -b + 4 -------------1

product of its roots = c/a

m*n = c/a

-4/5 * n = 12/5

-4 n = 12

n = -3 -------------2

Plug-in equation 2 in 1

5(-3) = -b + 4

-15 = -b + 4

b = 4+15

b =19

Hope this helps! For any further doubts you can message me, i am here to clarify

Answer 3

Because one of your Roots is a fraction, the easiest way to solve the quadratic is by using the Quadratic Formula, by which each Root (or Zero, or Solution) = [-b +/- SQRT(b^2 - 4ac)] / 2a when the equation is in standard form.

In your quadratic: a = 5 and c = 12

Solve for b: -4/5 = [-b +/- SQRT(b^2 - 4(5)(12))} / 2(5)

-4/5 = [ -b +/- SQRT ( b^2 -240) ] /10 Mult both sides by 10

-8 = -b +/- SQRT( b^2 - 240) Add b to both sides

b-8 = +/- SQRT (b^2 - 240) Square both sides to remove the radical (SQRT means square root)

(b-8)^2 = b^2 - 240

b^2 -16b + 64 = b^2 -240 Subtract b^2 from both sides

-16b + 64 = -240 Add 240 to both sides and Add 16b to both sides

240 + 64 = 16b

304 = 16b

19 = b

Check it: 5x^2 +19x + 12 has factors (5x + 4 )(x + 3 ) Roots are (-4/5, -3)

Answer 4

I just did it for you. Look down for the solution.