Question

7. Find the zeros of the polynomial 2x^2+4x-6 and verify the relationship between
the zeros and their coefficients.​

Answer 1

2x² + 4x - 6

________ [GIVEN EQUATION]

• We have to find the zeros of the above polynomial.

=> 2x² + 4x - 6 = 0

Here,

a = 2

b = 4

and c = - 6

• Take 2 common from L.H.S.

=> 2(x² + 2x - 3) = 0

=> x² + 2x - 3 = 0

=> x² + 3x - x - 3 = 0

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

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

=> x - 1 = 0

=> x = + 1

Similarly

=> (x + 3) = 0

=> x = - 3

______________________________

Zeros are :

+ 1 and - 3

_______________________________

• Sum of roots = $\dfrac{- b}{a}$

=> + 1 + (-3) = $\dfrac{-4}{2}$

=> 1 - 3 = - 2

=> - 2 = - 2

_______________________________

• Product of roots = $\dfrac{c}{a}$

=> (1) × (-3) = $\dfrac{-6}{2}$

=> - 3 = - 3

_______________________________

Answer 2

2x² + 4x - 6 = 0

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

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

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

x = + 1, - 3

Sum of roots = -b/a

- 2 = -2

Product of roots = c/a

- 3 = - 3