Which of the following is false?
(i) If only the positive values of x are taken, the quadratic graph does not intersect the K-axis.
(ii) if only negative values are taken, the quadratic graph does not intersect the X-axis.
(iii)The intercept of X-axis can be known when we substitute x =0, in the quadratic function.
(iv)There can be minimum zero and maximum two x-intercepts .

Options

A. (A) (i) and (iv)
B. (B) (i),(ii),(iii)and (iv)
C. (C) (i),(ii) and (iii)
D. (D) none of these

Answer

To determine which of the statements is false, we will analyze each statement one by one based on the properties of quadratic equations.

### Step 1: Analyze Statement (i)
**Statement (i):** If only the positive values of x are taken, the quadratic graph does not intersect the x-axis.

- A quadratic function is given by \( y = ax^2 + bx + c \).
- The graph intersects the x-axis where \( y = 0 \), which means we need to find the roots of the equation \( ax^2 + bx + c = 0 \).
- The nature of the roots depends on the discriminant \( D = b^2 - 4ac \).
- If \( D < 0 \), the quadratic does not intersect the x-axis at all, regardless of whether x is positive or negative.
- Therefore, this statement is **false** because the intersection depends on the discriminant, not the values of x being positive.

### Step 2: Analyze Statement (ii)
**Statement (ii):** If only negative values are taken, the quadratic graph does not intersect the x-axis.

- Similar to the first statement, the intersection of the graph with the x-axis depends on the discriminant \( D \).
- If \( D < 0 \), the quadratic does not intersect the x-axis, but this is not dependent on whether x is negative or positive.
- Hence, this statement can also be **false** in certain cases, but it is not universally false as the first statement.

### Step 3: Analyze Statement (iii)
**Statement (iii):** The intercept of the x-axis can be known when we substitute \( x = 0 \) in the quadratic function.

- The x-intercepts are found by setting \( y = 0 \) in the equation \( y = ax^2 + bx + c \).
- Substituting \( x = 0 \) gives \( y = c \), which provides the y-intercept, not the x-intercept.
- Therefore, this statement is **false**.

### Step 4: Analyze Statement (iv)
**Statement (iv):** There can be a minimum of zero and a maximum of two x-intercepts.

- A quadratic can have:
- 0 x-intercepts (when \( D < 0 \)),
- 1 x-intercept (when \( D = 0 \), which means the graph touches the x-axis),
- 2 x-intercepts (when \( D > 0 \)).
- Thus, this statement is **true**.

### Conclusion
Based on the analysis:
- Statement (i) is false.
- Statement (ii) can be false but is not universally false.
- Statement (iii) is false.
- Statement (iv) is true.

Thus, the false statements are (i) and (iii).

### Final Answer
The false statements are (i) and (iii).