Find the zeroes of the polynomial 3x2 + 4x – 4., and verify the rel

1.	Find the zeroes of the polynomial 3x2 + 4x – 4., and verify the relation between the coefficients and the zeroes of the polynomial.
Answer» 3x² + 4x – 4 Splitting the middle term, we get, 3x² + 6x – 2x – 4 Taking the common factors out, we get, 3x(x+2) -2(x+2) On grouping, we get, (x+2)(3x-2) So, the zeroes are, x+2=0 ⇒ x= -2 3x-2=0⇒ 3x=2⇒x=2/3 Therefore, zeroes are (2/3) and -2 Verification: Sum of the zeroes = – (coefficient of x) ÷ coefficient of x² α + β = – b/a – 2 + (2/3) = – (4)/3 = – 4/3 = – 4/3 Product of the zeroes = constant term ÷ coefficient of x² α β = c/a Product of the zeroes = (- 2) (2/3) = – 4/3

Find the zeroes of the polynomial 3x2 + 4x – 4., and verify the relation between the coefficients and the zeroes of the polynomial.

Answer»

3x² + 4x – 4

Splitting the middle term, we get,

3x² + 6x – 2x – 4

Taking the common factors out, we get,

3x(x+2) -2(x+2)

On grouping, we get,

(x+2)(3x-2)

So, the zeroes are,

x+2=0 ⇒ x= -2

3x-2=0⇒ 3x=2⇒x=2/3

Therefore, zeroes are (2/3) and -2

Verification:

Sum of the zeroes = – (coefficient of x) ÷ coefficient of x²

α + β = – b/a

– 2 + (2/3) = – (4)/3

= – 4/3 = – 4/3

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

Product of the zeroes = (- 2) (2/3) = – 4/3