Question

5. Find the zeroes of the quadratic polynomial 3x^2 - x - 4 and verify the relationship between the zeroes and the coefficients.

Standard:- 10

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Answer 1

Heya!!!

p(x) = $3x^{2}$ - 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,

 
$3x^{2}$ - x - 4
$3x^{2}$  + 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 !!! 

Answer 2

The answer is explained in the attachment.


Hope it helps!