Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the cofficients 3x²-x-4

Answer 1

Answer:

p(x) = 3x^{2}3x

2

- x - 4

Here, a = 3, b = - 1 and c = - 4

Now,

Sum of zeroes = - b / a

= - (- 1) / 3

= 1 / 3

Product of zeroes = c / a

= - 4 / 3

Now,

As not other data is given, we will find zeroes by middle term splitting

So,

3x^{2}3x

2

- x - 4

3x^{2}3x

2

+ 3x - 4x - 4

3x (x + 1) - 4 (x + 1)

(3x - 4) (x + 1)

3x - 4 =

3x = 4

x = 4 / 3

and

x + 1 = 0

x = - 1

So,

The zeroes are 4 / 3 and - 1

Now,

Sum of zeroes = 4 / 3 + (- 1)

= 4 / 3 - 1

= 4 - 3 / 3

= 1 / 3

Product of zeroes = 4 / 3 × - 1

= - 4 / 3

Hence Verified !!!

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

3X²-X-4

=3X²+3X-4X-4

=3x(x+1)-4(x+1)

=(3X-4)(x+1)

X=4/3 &x=-1

Sum of zeroes=4/3-1= (4-3)/3=1/3=-b/ a

Product of zeroes =4/3×-1 =-4/3=c/a

Hence, verified.

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