Find the degree of the following polynomial
(i) \(7y^{ 5 }+6y^{ 2 }-1\)
(ii) \(\frac { y^{ 4 }+3y^{ 2 }+y }{ y } \)

4

(a)

If 2 is a zero of polynomial f(x)=ax²-3(a-1)x-1, then find the value of a.

4

(a)

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

4

(a)

If α and β are the zeroes of the polynomial 2y²+7y+5, then find the value of α+β+αβ.

4

(a)

Find the quadratic polynomial, whose sum of zeroes is 8 and their products is 12. Then, find the zeroes of the polynomial.

4

(a)

If 1 and -1 are zeroes of polynomial Lx⁴+Mx³+Nx²+Rx+P, then show that L+N+P=M+R.

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)

Obtain all other zeroes of the polynomial x⁴+7x³+7x²-35x-60, if two of its zeroes are -3 and -4.

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)

Find other zeroes of the polynomial 2x⁴-3x³-5x²+9x-3, if it is given that two of its zeroes are \(-\sqrt { 3 } \) and \(\sqrt { 3 } \) , respectively

4

(a)

If polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, then what will be the quotient and remainder?

4

(a)

The graph of y=p(x) is given, where p(x) is a polynomial. Find the number of zeros of p(x).

4

(a)

Polynomial x⁴ + 7x³ + 7x² + px + q is exactly divisible by x² + 7x + 12, then find the value of p and q.

4

(a)

If \(\alpha\) and \(\beta\) are the zeroes of polynomial p(x) = 3x² + 2x + 1, find the polynomial whose zeroes are \(\frac { 1-\alpha }{ 1+\alpha } \) and \(\frac { 1-\beta}{ 1+\beta} \)

4

(a)

If \(\alpha\) and \(\beta\) are zeroes of the polynomial p(x) = 6x² - 5x + k such that \(\alpha-\beta=\frac{1}{6}\), find the value of k.

4

(a)