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Zeros of a Polynomial

The degree of...

Question

The degree of a polynomial p(x) is ‘b’ (> 0).It cuts the graph of y = p(x) on X axis ‘a’ times, then $\frac{b}{a} \leq 1$ .

A

False

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B

True

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Solution

The correct option is A False

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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. 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.

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).

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