Number of Zeroes

Q.

If a polynomial cuts the x-axis at 3 points and y-axis at 2 points, then the number of zeroes of the polynomial would be

___

Q.

If a polynomial of the form y = f(x) cuts the X-axis at $3$ points and Y-axis at $2$ points, then the number of zeroes of the polynomial would be ___

Q.

If f(x) = (x - a)(x - b) , then if a and b are the zeros of the polynomial f(x), f(a) = f(b).

1. True

2. False

Q.

Find the zero the polynomial, $t\left(x\right)=px,p\ne 0$

Q.

If k and 2k are zeros of $f\left(x\right)=x^3+4x^2+9kx=90$, find k and all three zeros of f(x).

1. K = 1, roots = -3, -6, -5

2. K = -3, roots = -3, -6, 5

3. K = -3, roots = -3, 6, -5

4. K = 3, roots = -3, -6, 5

Q. The number of zeroes, the polynomial $x^7+x^5+x^3+x+1$ can have is equal to .

1. 7
2. 5
3. 3
4. 1

Q.

The maximum number of zeroes the polynomial $x^7+x^5+x^3+x+1$ can have is _______.

1. 0

2. 6

3. 5

4. 7

Q. The number of zeroes of the polynomial $p\left(x\right)$ shown in the given graph is

1. $5$
2. $6$
3. $3$
4. $4$

Q. How many zeros can the polynomial
$p\left(x\right)=x^5+4x^4+3x^2+2x+1$
have at most?

1. 5

Q. Find the roots of the following quadratic equation by the method of completing the square:
$2x^2+x-4=0$

1. $\frac{\sqrt{35}-1}{4}$ or $x=\frac{-\sqrt{35}-1}{4}$
2. $\frac{\sqrt{33}-1}{2}$ or $x=\frac{-\sqrt{33}-1}{2}$
3. $\frac{\sqrt{35}-1}{2}$ or $x=\frac{-\sqrt{35}-1}{2}$
4. $\frac{\sqrt{33}-1}{4}$ or $x=\frac{-\sqrt{33}-1}{4}$

Q. Arrange the following polynomials in ascending order of the maximum number of zeros they can have.

1. $x^6+4x^3+5$
2. $x^{16}+24x^3$
3. $x^{99}+1$
4. $x^{100}-1$

Q. Find the maximum number of zeroes of the given polynomial.
$x^{10}+x^6+x^4+x+1$

1. 6
2. 5
3. 4
4. 10

Q. The number of zeroes, the polynomial $x^7+x^5+x^3+x+1$ can have is equal to .

1. 7
2. 5
3. 3
4. 1

Q. The number of zeroes, the polynomial $x^7+x^5+x^3+x+1$ can have is equal to .

1. 7
2. 5
3. 3
4. 1

Q.

In the method to find the roots of the quadratic equation 3$x^2$- 2$\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

1. - $\sqrt{3}$, $\sqrt{6}$

2. $\sqrt{3}$, -$\sqrt{2}$

3. - $\sqrt{7}$, $\sqrt{6}$

4. $\sqrt{3}$, $\sqrt{6}$

Q. Arrange the following polynomials in ascending order of the maximum number of zeros they can have.

1. $x^6+4x^3+5$
2. $x^{16}+24x^3$
3. $x^{99}+1$
4. $x^{100}-1$

Q.

In the method to find the roots of the quadratic equation 3$x^2$- 2$\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The values of a and d are

1. $\sqrt{3}$, -$\sqrt{2}$

2. $\sqrt{3}$, $\sqrt{6}$

3. - $\sqrt{3}$, $\sqrt{6}$

4. - $\sqrt{7}$, $\sqrt{6}$

Q. Arrange the following polynomials in ascending order of the maximum number of zeros they can have.

1. $x^{16}+24x^3$
2. $x^{100}-1$
3. $x^{99}+1$
4. $x^6+4x^3+5$

Q.

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorisation method.

1. $\frac{5}{\sqrt{2}}$ and - $\sqrt{2}$

2. $\frac{-5}{\sqrt{2}}$ and $\sqrt{2}$

3. $\frac{5}{\sqrt{2}}$ and $\sqrt{2}$

4. $\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$

Q.

According to the adjoining graph, the product of the zeroes of the polynomial will be

1. negative

2. zero

3. cannot be determined

4. positive

Q. How many zeros can the polynomial
$p\left(x\right)=x^5+4x^4+3x^2+2x+1$
have at most?

1. 5

Q. The number of zeroes, the polynomial $x^7+x^5+x^3+x+1$ can have is equal to .

1. 7
2. 5
3. 3
4. 1

Q. The number of zeroes, the polynomial $x^7+x^5+x^3+x+1$ can have is equal to .

1. 7
2. 5
3. 3
4. 1

Q. Find the roots of the following quadratic equation by the method of completing the square:
\( 2x^2 + x - 4 = 0\)