STATEMENT -1 : From the given graph of y $=$ p(x), number of zeroes of p(x) is 1.
STATEMENT -2 : The number of points where the graph cuts the x-axis gives the zeroes of any polynomial p(x).

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

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Statement - 1 is True, Statement - 2 is False

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Statement - 1 is False, Statement - 2 is True

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Solution

The correct option is D Statement - 1 is False, Statement - 2 is True
We know that the number of points where the graph cuts the x-axis gives the zeroes of any polynomial p(x). Since the polynomial is a linear line parallel to x-axis and is not cutting the x-axis at any point, therefore this polynomial has no zeroes/roots.

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Similar questions

- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

a > 1

- 2 :

a > 1, {log}_{a} x

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

Statement 1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement 2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

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