Question

find the product of the zeros of the polynomial p(x)=3x^-7x-15​

Answer 1

CORRECT QUESTION:

Find the product of roots of the polynomial

p( x ) = 3x² - 7x - 15

ANSWER:

Given polynomial

p( x ) = 3x² - 7x - 15

Let the roots of the given polynomial be α , β

TO FIND:

Product of roots of the given polynomial

p( x ) = 3x² - 7x - 15 . That means to find αβ

Using quadratic equation formula ↓

x = -b ± √b² - 4ac/2a

Here,

a = 3 , b = - 7 , c = - 15

♦ x = -( - 7) ± √(-7)² - 4(3)(-15)/2(3)

♦ x = 7±√49 + 180/6

♦ x = 7 ± √229/6

♦ x = 7+√229/6 ( or ) 7 - √229/6

Hence , α = 7 + √229/6 , β = 7 - √229/6

To find : αβ

→ αβ = (7 + √299)(7 - √229)/6²

Using

(a + b)(a - b) = a² - b²

→ αβ = 7² - (√299)²/36

→ αβ = 49 - 299/36

→ αβ = - 250/36

Hence, Product of the roots = - 250/36