Question

Find the zeros of the polynomial and verify the relationship between the zeros and the cofficient of the polynomial,2x²-x-6

Answer 1

Solution:

Given Polynomial : 2x²-x-6

Let polynomial be f(x) = 2x²-x-6

f(x) = 2x²-x-6

f (0)= 2x²-x-6 = 0

☞ 2x²-x-6 = 0

☞ 2x² -4x + 3x - 6 = 0

☞ 2x(x - 2) + 3(x - 2) = 0

☞ (2x -2) ( x - 2) = 0

°•° f(x) = 2x -2 = 0 0r f(x) = x - 2= 0

☞ 2x = 2 0r ☞ x = 2

☞ x = 1

Now, Verify Relationship between Zeroes:

Sum of Zeros ( à + ß) = -b/a ☞ - ( Coefficient of x)/(Coefficient of x² )

☞ 1 + 2 = 1/2

Product of Zeros (àß) = c/a ☞ ( Constant term )/(Coefficient of x²)

☞ 1× 2 =- 6/2

☞ 2 = -3

Note : This Polynomial can't be verified.

Answer 2

a=2

b=-1

c=-6

Sum= -1

Product=2×-6 =-12

2x^2-4x+3x-6=

2x(x-2)+(x-2)

(x-2) (2x+3)

2x-2 =0

(x-2)=0

2x-2=0

x-2=0