Find the zeroes of the polynomial 2x2 + 7/2 x + 3/4, and verify the re

1.	Find the zeroes of the polynomial 2x2 + 7/2 x + 3/4, and verify the relation between the coefficients and the zeroes of the polynomial.
Answer» 2x² +(7/2)x +3/4 The equation can also be written as, 8x²+14x+3 Splitting the middle term, we get, 8x²+12x+2x+3 Taking the common factors out, we get, 4x (2x+3) +1(2x+3) On grouping, we get, (4x+1)(2x+3) So, the zeroes are, 4x+1=0 ⇒ x = -1/4 2x+3=0 ⇒ x = -3/2 Therefore, zeroes are -1/4 and -3/2 Verification: Sum of the zeroes = – (coefficient of x) ÷ coefficient of x² α + β = – b/a (- 3/2) + (- 1/4) = – (7)/4 = – 7/4 = – 7/4 Product of the zeroes = constant term ÷ coefficient of x² α β = c/a (- 3/2)(- 1/4) = (3/4)/2 3/8 = 3/8

Find the zeroes of the polynomial 2x2 + 7/2 x + 3/4, and verify the relation between the coefficients and the zeroes of the polynomial.

Answer»

2x² +(7/2)x +3/4

The equation can also be written as,

8x²+14x+3

Splitting the middle term, we get,

8x²+12x+2x+3

Taking the common factors out, we get,

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

On grouping, we get,

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

So, the zeroes are,

4x+1=0 ⇒ x = -1/4

2x+3=0 ⇒ x = -3/2

Therefore, zeroes are -1/4 and -3/2

Verification:

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

α + β = – b/a

(- 3/2) + (- 1/4) = – (7)/4

= – 7/4 = – 7/4

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

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

3/8 = 3/8