Polynomial Questions

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :

Question : Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following : (i)  p(x) = $$x^3 – 3x^2 + 5x – 3$$,  g(x) = $$x^2 – 2$$ (ii)  p(x) = $$x^4 – 3x^2 + 4x + 5$$, g(x) = $$x^2 + 1 – x$$ …

Find a quadratic polynomial whose sum of zeroes and product of zeroes are respectively.

Question : Find a quadratic polynomial whose sum of zeroes and product of zeroes are respectively. (i)  $$1\over 4$$, -1 (ii)  $$\sqrt{2}$$, $$1\over 3$$ (iii)  0, $$\sqrt{5}$$ (iv)  1, 1 (v)  $$-1\over 4$$, $$1\over 4$$ (vi)  4, 1 Solution : Let the polynomial be $$ax^2 + bx + c$$ and its zeroes be $$\alpha$$ and …

Find the zeroes of the quadratic polynomials and verify a relationship between zeroes and its coefficients.

Question : Find the zeroes of the quadratic polynomials and verify a relationship between zeroes and its coefficients. (i)  $$x^2 – 2x – 8$$ (ii)  $$4s^2 – 4s + 1$$ (iii)  $$6x^2 – 3 – 7x$$ (iv)  $$4u^2 + 8u$$ (v)  $$t^2 – 15$$ (vi)  $$3x^2 – x – 4$$ Solution : (i)  \(x^2 – …

The graph of y = p(x) are given below, for some polynomial p(x). Find the number of zeroes of p(x), in each case.

Question : The graph of y = p(x) are given below, for some polynomial p(x). Find the number of zeroes of p(x), in each case. Solution : (i)  There are no zeroes as the graph does not intersect the x-axis. (ii)  The number of zeroes is one as the graph intersect the x-axis at one point …