SOLUTION: 12. Given the quadratic equation: X(to the 2nd power) -5X +1 = 0 a. what is the sum of the roots? b. What is the product of the roots? 13. Write a quadratic equation such tha

Question 205728This question is from textbook Book 1 Modern Algebra Structure and Method
: 12. Given the quadratic equation: X(to the 2nd power) -5X +1 = 0
a. what is the sum of the roots?
b. What is the product of the roots?
13. Write a quadratic equation such that the sum of the roots is 6 and the product of the roots is -11.
14, One number is 14 more than another number. Their product is 351. What are the numbers.
Thank you very much...please help me! This question is from textbook Book 1 Modern Algebra Structure and Method

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
x^2 -5x +1
.
solve for roots using quadratic eqn
.
a=1,,,,b=(-5),,,,,c=1
.
x= [-(-5) +/- sqrt{(-5)^2 -4(1)(1)}] / 2(1)
.
x=[ 5+/- sqrt{25-4}]/2
.
x=[ 5+/- 4.583}/2
.
x= 4.79,,,.209
.
a) sum = 4.79 +.209 = 5
.
b) product = (4.79)(.209) =1
.
(13) (1) x + y =6,,,,,,x=6-y
.
(2) xy = -11
.
substitute in (2) (6-y)(y) - -11
.
6y -y^2 =-11
.
y^2 -6y -11 =0
.
check, solving using quadratic eqn, y= 7.472, -1.472,,,
.
7.472 -1.472 =6,,,ok,,,,,,,,,,,,,7.472*-1.472 = -11,,,ok
.
14),,(1) x=y+14
.
(2) xy = 351
.
substitute (1) into (2)
.
(y+14)(y) =351
.
y^2 +14y -351 =0
.
(y+27)(y-13) =0
.
y= -27,,,+13,,,,,,,,x= -13, 27
.
solutions (27,13),,,(-13,-27)
.
check,,,,27 = 13+14,,,ok,,,,27*13 = 351
.
-13 = -27 +14,,,ok,,,,,,,,,,-13*-27 = +351,,,,ok
.

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