If \(\alpha\) and \(\beta\) are the roots of ax² - bx + c = 0 \(\left( a\neq 0 \right) \), then calculate \(\alpha+\beta\).

If sum of the zeroes of the quadatic polynomial 3x² - kx + 6 is 3, then find the value of k.

If - 1 is a zero of the polynomial f(x) = x² - 7x - 8, then calculate the other zero.

If the product of the zeroes of the polynomial (ax²-6x-6) is 4, then find the value of a.

If one zero of the polynomial (a²+9)x²+13x+6a is a reciprocal of the other, then find the value of a.

If zeroes of the polynomial x² + 4x + 2a are \(\alpha\) and \(\frac{2}{\alpha}\), then find the value of a. 

If p,q are zeroes of polynomial f(x) = 2x² - 7x + 3, find the value of p² + q².

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of p and q.

If the squared difference of the zeroes of the quadratic polynomial f(x) = x² + px + 45 is equal to 144, find the value of p.

Find the value of 'a' if X+a is a factor (zero) of the polynomial 2x²+2ax+5x+10.

Find the quadratic polynomial, whose zeroes are in the ratio 2:3 and their sum is 15.

In the given figure, the graph of a polynomial p(x) is shown. Find the number of zeros of P(x).

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial 6y² - 7y + 2, find a quadratic polynomial whose zeroes are \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\)

When p(x) = x² + 7x + 9 is divided by g(x), we get (x + 2) and - 1 as the quotient and remainder respectively, find g(x).

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

Represent the following quadratic polynomial on the graph and also find the zeroes of the polynomial
-x²+x+6

Divide the polynomial p(x) by the polynomial g(x) and verify the division algorithm in following.
 p(x)=2x⁴-2x³-5x²-x+8, g(x)=2x²+4x+3

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

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.