Polynomials Test

The number of zeroes of a cubic polynomial is

The maximum number of zeroes that a polynomial of degree 3 can have is

If \(\alpha \;\;and\;\;\beta \) are the zeroes of the polynomial \(2{x^2} + 5x + 1\), then the value of \(\alpha + \beta + \alpha \beta \) is

If one zero of the polynomial \(p(x) = ({a^2} + 9){x^2} + 45x + 6a\) is reciprocal of the other, then the value of ‘a’ is

The sum and product of the zeroes of the polynomial \(f(x) = 4{x^2} - 27x + 3{k^2}\) are equal, then the value of ‘m’ is

If one of the zeroes of the quadratic polynomial \(14{x^2} - 42{k^2}x - 9\) is negative of the other, then the value of ‘k’ is

The third zero of the polynomial \({x^3} + 7{x^2} - 2x - 14\), if two of its zeroes are \(\sqrt 2 \) and \( - \sqrt 2 \), is

If \(\sqrt {\frac{5}{3}} \) and \( - \sqrt {\frac{5}{3}} \) are the two zeroes of the polynomial \(3{x^4} + 6{x^3} - 2{x^2} - 10x - 5\) then its other two zeroes are

If the product of two of the zeroes of the polynomial \(2{x^3} - 9{x^2} + 13x - 6\) is 2, then the third zero of the polynomial is

If the polynomial \(3{x^3} - 4{x^2} - 17x - k\) is exactly divisible by \(x - 3\), then the value of ‘k’ is

If \(x - 2\) is a factor of the polynomial \(3{x^3} - 7{x^2} + kx - 16\), then the value of ‘k’ is

On dividing the polynomial \(6{x^3} - 11{x^2} + 7x + 5\) by \(2x - 3\), the quotient is

On dividing the polynomial \({x^4} - 5x + 6\) by \(2 - {x^2}\), the remainder is

If \(x - 2\) is a factor of \({x^3} + a{x^2} + bx + 16\) and \(a - b = 6\), then the values of ‘a’ and ‘b’ are

If ‘3’ is a zero of the polynomial \(2{x^3} - {x^2} - 13x - 6\), then the remaining zeroes of the polynomial are