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Geometrical Meaning of Zeros of Polynomial

The number of...

Question

The number of times the graph of y = p(x) cuts the X axis is ‘a’. The degree of the polynomial p(x) is ‘b’ (> 0). Then $\frac{b}{a}$ ___ 1

A

<

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B

>

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C

\geq

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D

\leq

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Solution

The correct option is C $\geq$
The graph of y = p(x) with degree 'b' can cut the x axis a maximum of b times.It is given that it cuts the x axis a times. Hence a can be any integer from 0 to b. i.e. $0 < a \leq b . S o \frac{b}{a} \geq 1$ .

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Q. The number of times the graph of y = p(x) cuts the X axis is ‘a’. The degree of the polynomial p(x) is ‘b’ (> 0). Then

\frac{b}{a}

Q. The number of times the graph of y = p(x) cuts the X axis is ‘a’. The degree of the polynomial p(x) is ‘b’ (> 0). Then

\frac{b}{a}

Q. If a polynomial p(x) is of degree “n”, the graph of the polynomial should cut the X axis at “n” points.

Q. 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).

Q. Assertion :If p(x) is a polynomial of degree

\geq

1 and ax+b is a factor of p(x) then we have

p (- \frac{b}{a}) = 0

. Reason: If p(x) is a polynomial of degree

\geq

1, then polynomial (x-a)(x-b) is a factor of p(x) if p(a)=0 and p(b)=0.

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