What must be subtracted from p(x) = 8x⁴ + 14x³ - 2x² + 7x - 8 so that the resulting polynomial is exactly divisible by g(x) = 4x² + 3x - 2?

If α and β are the zeroes of the polynomial 2x² - 3x + 1, then the value of α² + β² is:

The product of the zeroes of the cubic polynomial p(x) = x³ - 7x + 6 is:

The sum of the zeroes of the cubic polynomial 2x³ - 5x² - 14x + 8 is:

The sum of the zeroes of the quadratic polynomial 3x² + 5x - 2 is:

The product of the zeroes of the quadratic polynomial 2x² - 9x + 4 is:

If two zeroes of the polynomial x⁴ - 6x³ - 26x² + 138x - 35 are 2 ± √3, the other two zeroes are:

A quadratic polynomial whose sum and product of zeroes are -3 and 2 respectively is:

If the zeroes of the polynomial 5x² + 13x + k are reciprocal of each other, then the value of k is:

On dividing x³ - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x-2 and -2x+4 respectively. Then g(x) is:

If the graph of a quadratic polynomial lies entirely above the x-axis, then it has:

If the zeroes of the quadratic polynomial x² + (a+1)x + b are 2 and -3, then:

If 1 is a zero of the polynomial p(x) = ax² - 3(a-1)x - 1, then the value of 'a' is:

Which of the following expressions is a polynomial?

The degree of the polynomial p(x) = 7x³ - 4x⁵ + 2x + 9 is:

The sum of the digits of a two-digit number is 9. If 27 is added to the number, its digits are reversed. The number is:

The pair of equations 3x - 5y = 7 and -6x + 10y = 7 has:

A father's age is six times his son's age. Four years hence, the father's age will be four times his son's age. The present ages of the son and the father are, respectively: