Polynomials

1 Mark and 2 Mark questions :

1) Find the value of 'm' in order that x⁴-2x³+3x²-mx+5 may be exactly divisible by (x-1)

2) Comment the roots of the quadratic equation 3x²-7x+2=0

3) Find the roots of the equation x²+x(c-b)+(c-a)(a-b)=0

4) If x³-3x²+4x+k is divisible by (x-2) find the value of k

5) Find the sum and product of the roots of the equation √3x² +9x+6√3 =0

6) State and prove the reminder Theorem.

7) Find the reminder, When x ⁴+4x³-5x²-6x+7 is divided by (x+3),(x-3)

8)  Find the Quadratic equation whose roots are i) 2 and 3 ii) 2+√3,2-√3

9) Find the value of k so that x³-3x²+4x+k is exactly divisible by x-2

10) find the middle term of(x/y + y/x)⁸

^{11) Find the Quadratic Equation in x ,Which when divided by (x-1),(x-2) and (x-3) leaves the reminder of 11 ,22 and 39 respectively..}

4 Mark Questions :

12) find the constant term in the expansion (3x-(5/x²))⁹

13) factorize the following i) x⁴+5³+5²-5x-6  ii) 3x⁴-10x³+5x²+10x-8

14) find the independent term of 'x' (6x-( (5/x²))¹²

15)find the values of 'b' and 'c' ,if divison of x²+bx+c by i)x-1 leaves the reminder zero ii) x+2 leaves the reminder 12

16) if f(x)=x²+5x+p and q(x)=x²+3x+q have common factor then i) find the common factor ii) show that (p-q)²=2(3p-5q)

 5 Mark Questions :

17) solve x²-4x+3=0 using the graph of y=x²

18) solve x²-x-2=0 using the graph of y=x²

19) solve x²-3x+2=0 using the graph of y=x²

20) Draw Graph for y=x²-5x+6 and solve x²-5x+6=0

21)  Draw Graph for y=x²+5x+6