Write a rational expression in x in which the zeros of the polynomial in numerator 2 and -1, while the zeros of the polynomial in denominator are -2 and 1, the coefficient of $x^{2}$ being 1 in both the numerator as well as thedenominator

\frac{x^{2} + x - 2}{x^{2} + x + 2}

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\frac{x^{2} - x - 2}{x^{2} - x - 2}

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\frac{x^{2} - x - 2}{x^{2} + x + 2}

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\frac{x^{2} - x - 2}{x^{2} + x - 2}

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Solution

The correct option is D $\frac{x^{2} - x - 2}{x^{2} + x - 2}$
The zeros of the polynomial in numerator are 2 and -1 with coefficient of x $^{2}$ being 1.
$∴$ The numerator $p (x) = (x - 2) [x - (- 1)]$

$= (x - 2) (x + 1) = x^{2} - x - 2$

The zeros of the polynomial in denominator are -2 and 1 with coefficient of $x^{2}$ being 1.
$∴$ The denominator $q (x) = [x - (- 2)] (x - 1)$

$= (x + 2) (x - 1) = x^{2} + x - 2$

Then , the required rational expression $= \frac{p (x)}{q (x)} = \frac{x^{2} - x - 2}{x^{2} + x - 2}$

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Similar questions

Which of the following expressions is a polynomial ?
(a) $\sqrt{x} - 1$
(b) $\frac{x - 1}{x + 1}$
(c) $x^{2} - \frac{2}{x^{2}} + 5$
(d) $x^{2} + \frac{2 x^{\frac{3}{2}}}{\sqrt{x}} + 6$

Question 1
Which one of the following is a polynomial?

A) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$
B) $\sqrt{2 x} - 1$
C) $x^{2} + \frac{3 x^{\frac{3}{2}}}{\sqrt{x}}$
D) $\frac{x - 1}{x + 1}$

Q. Question 2
A quadratic polynomial, who zeroes are -3 and 4, is
(a)

x^{2} - x + 12

(b)

x^{2} + x + 12

(c)

\frac{x^{2}}{2} - \frac{x}{2} - 6

(d)

2 x^{2} + 2 x - 24

Verify that
(i) 1 and 2 are the zeros of the polynomial, $p (x) = x^{2} - 3 x + 2$ .
(ii) 2 and -3 are the zeros of the polynomial, $q (x) = x^{2} + x - 6.$
(iii) 0 and 3 are the zeros of the polynomial, $r (x) = x^{2} - 3 x$ .

Q. Which of the following polynomials has (x + 1) as a factor?
I.

x^{3} + x^{2} + x + 1

II.

x^{4} + x^{3} + x^{2} + x + 1

III.

x^{4} + 3 x^{3} + 3 x^{- 2} + x + 1

II.

x^{3} + x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

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Write a rational expression in x in which the zeros of the polynomial in numerator 2 and -1, while the zeros of the polynomial in denominator are -2 and 1, the coefficient of x2 being 1 in both the numerator as well as thedenominator

Write a rational expression in x in which the zeros of the polynomial in numerator 2 and -1, while the zeros of the polynomial in denominator are -2 and 1, the coefficient of $x^{2}$ being 1 in both the numerator as well as thedenominator