In the previous post, Our IB Maths Tutors have discussed how to solve a quadratic polynomial using the Quadratic formula. Here I will tell you about different relationships based on the sum and product of quadratic polynomial, cubic polynomial, and bi-quadratic polynomials.
ax2 + bx + c = 0
Sum of the roots = −b/a
The product of the roots = c/a
If we know the sum and product of the roots/zeros of a quadratic polynomial, then we can find that polynomial using this formula
x2 − (sum of the roots)x + (product of the roots) = 0
Now let us look at a Cubic (one degree higher than Quadratic):
ax3 + bx2 + cx + d=0
if α, β and γ are the zeros of this cubic polynomial then
If we know these relationships of polynomials then we cal also calculate the polynomial using this formula:
If we are given a bi-quadratic polynomial with degree 4 like:
and its roots/zeros are α, β, γ, and δ then
using these formulas of sum and product of zeros of polynomials, we can find a lot of relationships in zeros of polynomials. Usually, we are asked to find these types of relationships in zeros.
Question: If α and β are the zeros of polynomial x²-px+q=0 then find the following relationships.
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