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Standard IX

Mathematics

Zeroes of a Polynomial

Zero's of the...

Question

Zero's of the polynomial p(x) = $x^{2}$ -2x is / are :

0, 2

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0, 1

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1, 2

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2, 3

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Solution

The correct option is D 0, 2
Zeros of the polynomial $x^{2} - 2 x = p (x)$

$x^{2} - 2 x = 0$

$\Rightarrow x (x - 2) = 0$

$\Rightarrow x = 0$ or $x = 2$

$∴$ Zeros of polynomial $p (x)$ are $0$ and $2$

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Similar questions

Q. Verify that:
(i) 2 is a zero of the polynomial p(x) = (x

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2).
(ii) 2 and 9 are zeroes of the polynomial p(x) = (x

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2) (x

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(iii) 4 and

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3 are zeroes of the polynomial p(x) = x²

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12.

Q. A polynomial

p (x)

is divided by

g (x)

, the obtained quotient

q (x)

and the remainder

r (x)

are given in the table. Find

p (x)

in each case.

Sl.	$p (x)$	$g (x)$	$q (x)$	$r (x)$
i	?	$x - 2$	$x^{2} - x + 1$	$4$
ii	?	$x + 3$	$2 x^{2} + x + 5$	$3 x + 1$
iii	?	$2 x + 1$	$x^{3} + 3 x^{2} - x + 1$	$0$
iv	?	$x - 1$	$x^{3} - x^{2} - x - 1$	$2 x - 4$
v	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

Q. Determine the L.C.M and H.C.F of two polynomials,

p (x)

and

q (x)

are

(x^{2} - 9)

and

2 (x + 1)^{2}

respectively. If

p (x) = 12 (x + 1) (x - 3)

, find

q (x)

Q. Let

P (x)

be a polynomial with real coefficients such that

P ({sin}^{2} x) = P ({cos}^{2} x)

, for all

x ϵ [0, π / 2]

. Consider the following statements:
I.

P (x)

is an even function.
II.

P (x)

can be expressed as a polynomial in

(2 x - 1)^{2}

.
III.

P (x)

is a polynomial of even degree.
Then

Q. Find the zeroes of the polynomial

p (x) = x^{2} + 2 x

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Zero's of the polynomial p(x) =x2-2x is / are :

The correct option is D 0, 2Zeros of the polynomial x2−2x=p(x)x2−2x=0⇒x(x−2)=0⇒x=0 or x=2∴ Zeros of polynomial p(x) are 0 and 2

Zero's of the polynomial p(x) = $x^{2}$ -2x is / are :

The correct option is D 0, 2
Zeros of the polynomial $x^{2} - 2 x = p (x)$

$x^{2} - 2 x = 0$

$\Rightarrow x (x - 2) = 0$

$\Rightarrow x = 0$ or $x = 2$

$∴$ Zeros of polynomial $p (x)$ are $0$ and $2$