Suggested Experiments

Quadratic polynomial - Zeroes of the polynomial - geometrical meaning/ graphs.

* Draw graphs for quadratic polynomial ax2+ bx + c for various conditions

(i) a > 0     (ii) a < 0     (iii) a = 0     (iv) b > 0     (v) b < 0    (vi) b = 0     and comment on the graphs


WHAT WE HAVE DISCUSSED

 1. Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.

2. A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c, where a, b, c are real numbers with a ¹ 0.

3. The zeroes of a polynomial p(x) are the x-coordinates of the points where the graph of y = p(x) intersects the X-axis.

4. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.

5. If a and b are the zeroes of the quadratic polynomial ax2 + bx + c, a not equal to 0, then

∝ + Β = –b/a ,∝Β = c/a .

6. If ∝,Β, g are the zeroes of the cubic polynomial ax3 + bx2+ cx + d, a not equal to 0, then

∝ + Β + Γ = -b/a, ∝Β + ΒΓ + Γ∝ = c/d

and ∝ΒΓ = -d/a

7. The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there exist polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x),

where either r(x) = 0 or degree r(x) < degree g(x) if r(x) not equal to 0.





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