Question

Show that 0.2353535...= 0.235 can be expressed in the form of p/q, where p and q are integers and q is not equal to zero​

Answer 1

Given a number 0.2353535…….

We need to prove0.2353535…= 0.235‾can be expressed in the form of p/q, where p and q are integers and q ≠zero

Proof:

Let us assume that x=0.2353535…=0.235 ——————(i)

On Multiplying both sides by 100 of equation (i) we get,

100x=100×0.2353535…

100x=23.53535————–(ii)

Subtracting equation (i) from equation (ii) we get,

99x=23.53535…−0.2353535…

x= 23.33 / 99

x= 233/ 990

Hence, x=0.2353535…=0.235‾ can be expressed in the form of p/q as 233/ 990 and here q=990 (q≠zero)

Hence proved

Answer 2

Answer:

$\small\underline\mathcal\pink{Answer}$

Let the given polynomial be p(x) = 4x2 – 4x – 8

To find the zeroes, take p(x) = 0

Now, factorise the equation 4x2 – 4x – 8 = 0

4x2 – 4x – 8 = 0

4(x2 – x – 2) = 0

x2 – x – 2 = 0

x2 – 2x + x – 2 = 0

x(x – 2) + 1(x – 2) = 0

(x – 2)(x + 1) = 0

x = 2, x = -1

So, the roots of 4x2 – 4x – 8 are -1 and 2.

Relation between the sum of zeroes and coefficients:

-1 + 2 = 1 = -(-4)/4 i.e. (- coefficient of x/ coefficient of x2)

Relation between the product of zeroes and coefficients:

(-1) × 2 = -2 = -8/4 i.e (constant/coefficient of x2)