Question

Find the zeroes of following quadratic polynomial and verify the relationship between the zeros and coefficient of 3x²+5x-2

Answer 1

3x²+5x-2

= 3x² + 6x − x − 2

= 3x(x + 2) − (x + 2)

= (x + 2)(3x - 1)

• x + 2 = 0

x = -2

• 3x - 1 = 0

3x = 1

x = 1/3

•°• zeroes are -2 and 1/3

α = -2

β = 1/3

Sum of zeroes = α + β = -2 + (1/3)

= (-6 + 1)/3

= -5/3

Product of zeroes = α x β = -2(1/3)

= -2/3

Answer 2

Step-by-step explanation:

3x²-5x-2 = 0

3x²-6x+x-2=0

3x(x-2)+1(x-2)=0

(x-2)(3x+1)=0

x-2=0 ; 3x+1=0

x=2 ; x=-1/3

Therefore, the zeroes of the polynomial are 2 and -1/3

Let α(alpha) =2

β(beta) =-1/3

Sum of zeroes = α+β=2+(-1/3)

=2-1/3

=(6-1)/3

=5/3=-(-5)/3

=-(x coefficient)/x² coefficient

Product of zeroes=αβ=2(-1/3)=-2/3

=constant/x² coefficient