Algebra 2 HELP!! PLEASE HELP ME!!!! find quadratic equation for which the sum of the solutions is 1/8.........

Question

Find a quadratic equation for which the sum of the of the solutions is 1/8, and the product of the solutions is 4/15

Thank u guys sooo much!!!!

Answer 1

Note that by the quadratic formula, the solutions for x should be

x1 = [-b + sqrt(b^2 - 4ac)]/(2a) and
x2 = [-b - sqrt(b^2 - 4ac)]/(2a)

Added together,

x1 + x2 = -b/2a + -b/2a = -2b/2a = -b/a

That means -b/a = 1/8

Multiplied together,
(x1)(x2) = {[-b + sqrt(b^2 - 4ac)]/(2a)} {[-b - sqrt(b^2 - 4ac)]/(2a)}

(x1)(x2) = (b^2 - (b^2 - 4ac))/[4a^2]
(x1)(x2) = (4ac)/(4a^2) = c/a

But the product of the solutions should be 4/15, so
c/a = 4/15

So our two equations are

-b/a = 1/8
c/a = 4/15

Cross multiplying both

-8b = a
15c = 4a

a + 8b = 0
4a - 15c = 0

We're not going to have a unique solution; we're going to have infinitely many. Let's solve this one by eliminating the a variable.

4a + 32b = 0
4a - 15c = 0

32b + 15c = 0

Any non-zero values for b and c which satisfy 32b + 15c = 0 will work.

Answer 2

X^2 - 1/8 *x + 4/15 =0

In general in x^2 +px +q=0 if the roots are a and b

a+b=-p and a*b=q

Answer 3

sum of roots=1/8+4/15
=15+32/120
=47/120
product of roots=1/8* 4/15
=1/30
formula:
x^2 - (s.o.r.)x+(p.o.r)=0
x^2-47/120x+1/30=0
120x^2-47x+4=0 is the equation.

Answer 4

sum of roots=1/8+4/15
=15+32/120
=47/120
product of roots=1/8* 4/15 =1/30

use formula:
x^2 - (s.o.r.)x+(p.o.r)=0
x^2-47/120x+1/30=0
120x^2-47x+4=0 is the equation.

Answer 5

Recall that quadratic equation is formed using the following formula
x^2 - (sum of soln)*x + (product of soln) = 0
So, in your case, quad equa is
x^2 - x/8 + 4/15 =0
Simplifying them will become
120x^2 - 15x + 32 = 0

Answer 6

a quadratic eqn can be generally defined as

x^2-(a+b)x+ab where a,b are the solutions...

the qn is direct since we have sum of solutions a+b=1/8
and product of solutions is ab=4/15

so the eqn is x^2-(1/8)x+4/15

if u want to remove the fractions in the result we have to multiply the eqn by (8x15)

so the eqn boils down to (8x15)x^2-15x+32=0

so final eqn is 120x^2-15x+32.

Answer 7

assume
(x - a)(x - b) = x^2 - (a + b)x + ab
then your equation becomes
x^2 - (1/8)x + 4/15 = 0
To arrive at integer coefficients, multiply by 120:
120x^2 - 15x + 32 = 0

Answer 8

givens:
sum of roots (-b/a): 1/8
prod of roots (c/a): 4/15

now multiply 15 to 1/8 ==> 15/120
and multiply 8 to 4/15 ==> 32/120

therefore,
a = 120
b = -15
c = 4

equation = 120x^2 - 15x + 4

Answer 9

Nah. The reciprocal of 8/45 is 45/8, which, if divided, is 5.625. There are no integers that can add up to equal that; only decimals will work, and, as far as I know, decimals are not integers.. and neither are fractions, if you think those will work.