Square Root of Polynomials

Q. Question 1 (ix)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials

(ix) $y^2+\frac{3}{2}\sqrt{5}y-5$

Q. Finding the square root of the polynomial $x^4-4x^3+10x^2-12x+9.$

1. $|x^2-2x-3|$
2. $|x^2+2x+3|$
3. $|x^2-2x+3|$
4. $|x^2+2x-3|$

Q. Find the square root of the following expressions.

1. $\frac{4x{z}^2}{6y}$
2. $\frac{x^{2}z}{y^3}$
3. $\frac{x^{4}z}{y^2}$

Q. Find the square root of the polynomial using factorisation method: $y^8+\frac{1}{y^8}-2$.

1. $|y^3+\frac{1}{y^3}|$
2. $|y^4+\frac{1}{y^4}|$
3. $y^4+\frac{1}{y^4}$
4. $|y^2+\frac{1}{y^2}|$

Q. Finding the square root of the polynomial $16x^4-24x^3+25x^2-12x+4.$

1. $|4x^2-3x+2|$
2. $|4x^2-3x-2|$
3. $|4x^2+3x-2|$
4. $|4x^2+3x+2|$

Q. Find the zeroes of the following polynomial by factorisation method and verify the relation between the zeroes and the coefficients of the polynomials:

$y^2+\frac{3}{2}\sqrt{5}y-5$.

1. $-2\sqrt{5},\frac{\sqrt{5}}{2}$
2. $-2\sqrt{5},\frac{\sqrt{3}}{2}$
3. $-2\sqrt{5},\frac{\sqrt{11}}{2}$
4. $-2\sqrt{5},\frac{\sqrt{10}}{2}$

Q. Finding the square root of the polynomial $4x^4+8x^3+8x^2+4x+1.$

1. $|2x^2+2x+1|$
2. $|2x^2+2x-1|$
3. $|2x^2-2x+1|$
4. $|2x^2-2x-1|$

Q. Determine the square root of the polynomial using factorisation method: $\sqrt{\frac{81(x+y{)}^2(x-y{)}^8}{9(x-y{)}^4}}$ = ?

1. $\left|\right(x+y\left)\right(x-y{)}^2|$
2. $3\left|\right(x+y\left)\right(x-y{)}^2|$
3. $3\left|\right(x+y\left)\right(x-y{)}^4|$
4. $\left|3\right(x+y\left)\right(x-y{)}^2|$

Q. Square root of the poynomial is $\sqrt{(3x+2y{)}^2-24xy}$

1. $(3x-2y)$
2. $(3x+2y)$
3. $(2x-3y)$
4. $(2x+3y)$

Q. Evaluate $\frac{6x^2-x-2}{8x^2+6x+1}\times \frac{12x^2-13x-4}{12x^2-25x+12}$ [3 Marks]

Q. Determine the square root of the polynomial $x^4+2x^2{y}^2+y^4$. (Use factorisation method).

1. $|x^2+y^2$
2. $x^2-y^2$
3. $|x^2+y^2|$
4. $\left|\right(x^2+y^2{)}^2|$

Q. Square root of the expression $16a^2+9b^2-24ab+24a-18b+9$ is .

1. $|4a-3b+3|$
2. $|4a+3b+3|$
3. $|4a-3b-3|$
4. $|4a+3b-3|$

Q. What is the square root of $9y^4-6y^3+7y^2-2y+1$ using division method?

Q. Find the square root of following polynomial $(2x^2-5x+2)(3x^2-5x-2)(6x^2-x-1)$

1. $|(2x-1)(x-2)(3x+1)|$
2. $|(2x-1)(x+2)(3x+1)|$
3. $|(2x+1)(x-2)(3x+1)|$
4. None of these

Q. Square root of the expression $16a^2+9b^2-24ab+24a-18b+9$ is . (2 marks)

Q. Determine the square root of the polynomial: $x^4+4x^3+8x^2-8x+4$ using long division method.

1. $|x+2x+2|$
2. $|x^2+x+2|$
3. $|x^2+2x+2|$
4. $x^2+2x+2$

Q. Square root of the expression $16a^2+9b^2-24ab+24a-18b+9$ is .

1. $|4a-3b+3|$
2. $|4a+3b+3|$
3. $|4a-3b-3|$
4. $|4a+3b-3|$