Number of Zeros

Q.

Find a quadratic polynomial whose zeroes are $-4$ and $3$ and Verify the relation between zeroes and the coefficients.

Q. Given that the graph shown below has taken the maximum number of turns it could take. The given graph is of

1. Quadratic polynomial
2. Cubic polynomial
3. Linear Polynomial
4. Biquadratic Polynomial

Q. If one zero of the polynomial $3x^2-8x+2k+1$ is seven times the other, find the value of $k$.

1. $\frac{2}{3}$
   
2. $\frac{3}{4}$
   
3. $-1$
4. $\frac{3}{5}$
   

Q. The graph of y=p(x) is given below. The number of zeroes of polynomial p(x), is

1. 2
2. 1
3. 3
4. 0

Q.

Which of the following graph represents a quadratic polynomial which has sum of its zeroes is zero?

1. 

2. 

3. 

4. 

Q. $\text{A quadratic polynomial whose zeroes}\text{are}\frac{3}{4}\text{and}\frac{1}{2}\text{is}$

1. $\frac{8x^2-10x+3}{8}$
2. $\frac{10x^2-8x+3}{4}$
3. $\frac{8x^2+10x+3}{8}$
4. $\frac{10x^2+8x+3}{4}$

Q. The graph of a polynomial P(x) is as shown.
Find the number of zeroes for the given graph of the polynomial.

Q.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p\left(x\right)=2x^2-5x+7$, find a polynomial whose zeroes are of $(2\alpha +3\beta )$ and $(3\alpha +2\beta )$.

Q. How many zeroes can linear polynomial have?

1. 3
2. 2
3. 0
4. 1

Q. If $\alpha \text{and}\beta$ are the zeroes of $p\left(x\right)=4x^2+10x+k$ such that ${\alpha }^2+{\beta }^2+\alpha \beta =\frac{21}{4}$, then k =

1. 2
2. 4
3. - 12
4. 12

Q. Given that the graph shown below has taken the maximum number of turns it could take. The given graph is of a.

1. Quadratic polynomial
2. Cubic polynomial
3. Linear Polynomial

Q. Given that the graph shown below has taken the maximum number of turns it could take. The given graph is of

1. Quadratic polynomial
2. Cubic polynomial
3. Linear Polynomial
4. Biquadratic Polynomial

Q. If $4x^2-6x-m$ is divisible by $x-3$, the value of $m$ is exact divisor of

1. $20$
2. $45$
3. $9$
4. $36$