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