Polynomials Question (1 Viewer)

[Leffife]

Solve the equation 3x³ - 17x² - 8x + 12 = 0, given that the product of two of the roots is 4.

[FONT=arial, helvetica, clean, sans-serif]Let roots be A,B,C.[/FONT]

 

[Aykay]

AB = 4 [given]
ABC = -4 [products of roots]

therefore, c = -1 ------ (A)

A + B + C = 17/3 [sum of roots]

Using (A):

A + B = 20/3 ---- (B)

Sub (B) into AB = 4:

B(20B/3 - B) = 4

Using quadratic formula, B = 2/3 or 6

Therefore the roots are 2/3, 6 and -1.

 

[Timske]

ab = 4 [given]
abc = -4 [products of roots]

therefore, c = -1 ------ (a)

a + b + c = 17/3 [sum of roots]

using (a):

A + b = 20/3 ---- (b)

sub (b) into ab = 4:

b(20b/3 - b) = 4

using quadratic formula, b = 2/3 or 6

therefore the roots are 2/3, 6 and -1.

b(20/3-b)=4