## Find the zeroes of the quadratic polynomial 3x²–2 and verify the relationship between the zeroes and the coefficients.​

Question

Find the zeroes of the quadratic polynomial 3x²–2 and verify the relationship between
the zeroes and the coefficients.​

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1 month 2021-09-14T22:28:24+00:00 2 Answers 0 views 0

3x²-2=0

3x²=2

x=√2/3

x= -2/3 or 2/3

∝= √-2/3

β= √2/3

Sum of zeroes= -b/a

∝+β                 =  0/3

√-2/3+2/3          =0

√-2+2/3              =0

√0/3                  =0

0=0

product of zeroes=c/a

∝×β                       = -2/3

√-2/3×√2/3          = -2/3

√-4/9                    = -2/3

-2/3                       = -2/3

3x^2-2 is the given quadratic polynomial

To get zeroes of the polynomial we should equate to ‘zero 0’

3x^2-2=0

3x^2=2

x^2=2/3

x=root of (2/3) (OR) -root of(2/3)

Step-by-step explanation:

VERIFICATION :-

The relatin between zeroes and coefficients is

(i) Sum of zeroes=-(coefficient of x)/(coefficient of x^2)

Root (2/3)-root (2/3)=-0/3

0=0

(ii) Product of zeroes = constant / (coefficient of x^2)

Root of(2/3)×-root of(2/3)=-2/3

-[root of (2/3)]^2=-2/3

-2/3=-2/3

Hence verified