# WORKSHEL POLYNOMIALS 1. If one zero of a quadratic polynomial $\left(k x^{2}+3 x+k\right)$ is 2 , then the what is the value of $k$ ? 2. The graph of a polynomial is shown in Figure. What is the number of its zeroes? 3. Find the quadratic polynomial, the sum of whose zeroes is $-5$ and their product is 6 . 4. If one zero of the polynomial $\left(3 x^{2}+8 x+k\right)$ is the reciprocal of the other, then what is the value of $k$ ? 5. What is the value of $x$, for which the polynomials $x^{2}-1$ and $x^{2}-2 x+1$ vanish simultaneously? 6. Find a quadratic polynomial, whose zeroes are $-3$ and 4 ? 7. If the sum of the zeroes of the polynomial $p(x)=2 x^{3}-3 k x^{2}+4 x-5$ is 6 , then what is the value of $k$. 8. In given figure, the graph of a poly

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WORKSHEL POLYNOMIALS 1. If one zero of a quadratic polynomial $\left(k x^{2}+3 x+k\right)$ is 2 , then the what is the value of $k$ ? 2. The graph of a polynomial is shown in Figure. What is the number of its zeroes? 3. Find the quadratic polynomial, the sum of whose zeroes is $-5$ and their product is 6 . 4. If one zero of the polynomial $\left(3 x^{2}+8 x+k\right)$ is the reciprocal of the other, then what is the value of $k$ ? 5. What is the value of $x$, for which the polynomials $x^{2}-1$ and $x^{2}-2 x+1$ vanish simultaneously? 6. Find a quadratic polynomial, whose zeroes are $-3$ and 4 ? 7. If the sum of the zeroes of the polynomial $p(x)=2 x^{3}-3 k x^{2}+4 x-5$ is 6 , then what is the value of $k$. 8. In given figure, the graph of a polynomial $p(x)$ is shown. Calculate the number of zeroes of $p(x)$. 9. If zeroes of the polynomial $x^{2}+4 x+2 a$ are $a$ and $\frac{2}{a}$ then find the value of $a$. 10. If one of the zeroes of the quadratic polynomial $p(x)=14 x^{2}-42 k^{2} x-9$ is negative of the other, find the value of ' $k$ '. 11. If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x)=x^{2}-x-k$, such that $\alpha-\beta=9$, find $k$. 12. If $\alpha$ and $\beta$ are zeroes of $x^{2}-(k-6) x+2(2 k-1)$, find the value of $k$ if $\alpha+\beta=\frac{1}{2} \alpha \beta$. 13. Quadratic polynomial $2 x^{2}-3 x+1$ has zeroes as a and $b$. Now form a quadratic polynomial whose zeroes are $3 a$ and $3 b$. 14. Find the zeroes of the quadratic polynomial $5 x^{2}+8 x-4$ and verify the relationship between the zeroes and the coefficients of the polynomial. 15. Find the value for $k$ for which $x^{4}+10 x^{3}+25 x^{2}+15 x+k$ is exactly divisible by $x+7$. 16. If $a$ and $b$ are the zeroes of polynomial $p(x)=3 x^{2}+2 x+1$, find the polynomial whose zeroes are $\frac{1-a}{1+a}$ and $\frac{1-b}{1+b}$. 17. If $\beta$ and $\frac{1}{\beta}$ are zeroes of the polynomial $\left(a^{2}+a\right) x^{2}+61 x+6 a$. Find the value of $\beta$ and