Find the zeroes of quadratic polynomial y²+92y+1920.

4

(a)

If zeroes α and β of a polynomial x²-7x+k are such that α-β=1, then find the value of k.

4

(a)

If α and β are the zeroes of the quadratic polynomial f(x)=3x²-5x-2, then evaluate α³+β³.

4

(a)

If α and β are zeroes of the quadratic polynomial p(x)=6x²+x-1, then find the value of \(\frac { \alpha }{ \beta } +\frac { \alpha }{ \alpha } +2\left( \frac { 1 }{ \alpha } +\frac { 1 }{ \beta } \right) +3\alpha \beta \)

4

(a)

On dividing polynomial p(x) by 3x+1, the quotient is 2x-3 and the remainder is -2. Find p(x).

4

(a)

If the polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, the remainder comes out to be ax+b, then find the values of a and b.

4

(a)

A polynomial g(x) of degree zero is added to the polynomial 2x³+5x²-14x+10, so that it becomes exactly divisible by 2x-3. Find g(x).

4

(a)

If the polynomial f(x)=3x⁴-9x³+x²+15x+k is completely divisible by 3x²-5, then find the value of k and hence the other two zeroes of the polynomial.

4

(a)

Draw the graph of the polynomial -x²+4x-4 and find the zeroes of the polynomial.

4

(a)

Write the cubic polynomial, whose zeroes are \(2-2\sqrt { 5 } ,2+2\sqrt { 5 }\) and 1, respectively.

4

(a)