Question

find the zeroes of 2x square + 7/2 x + 3/4 and verify the relationship between the zeroes and the polynomials

Answer 1

Answer:

these is the answer which is given above

Answer 2

Given:

2x² + 7/2 x + 3/4

To Find:

Find the zeroes and  verify the relationship between the zeroes and the polynomials

Solution:

2x² + 7/2 x + 3/4 = 0

8x² + 14x + 3 = 0 ( Taking L.C.M)

8x² + 12x+2x + 3 = 0

4x(2x+3) + 1(2x+3) =0 ( Taking 4x common)

(4x+1) (2x+3) =0

Now,

4x+1 = 0

$x_{1}$ = -1/4

(2x+3) = 0

$x_{2}$ = -3/2

So, the two roots of the equation are -1/4 and -3/2

Now we will verify the zeroes and the polynomial

As we know,

Sum of zeroes of a polynomial = -b/a

Product of zeroes of a polynomial= c/a

where a = coefficient of x²

          b =  coefficient of x

          c = constant term

Sum of zeroes = $x_{1}$+$x_{2}$

 $x_{1}$+$x_{2}$ = -b/a

-1/4+(-3/2) = -14/8  

- 7/2 = -7/2

L.H.S = R.H.S          

Product of zeroes =  $x_{1}$$x_{2}$  

 $x_{1}$$x_{2}$  = c/a

(-1/4)(-3/2) = 3/8

3/8 = 3/8

L.H.S = R.H.S

Hence the zeroes of the polynomial are -1/4 and -3/2. The relationship between the zeroes and the polynomials is verified.