What is the relation between zeros …
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Posted by Harsh Kushwah 2 years, 10 months ago
- 3 answers
Armaan Armaan 2 years, 10 months ago
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Preeti Dabral 2 years, 10 months ago
Consider quadratic polynomial
P(x) = 2x2 – 16x + 30.
Now, 2x2 – 16x + 30 = (2x – 6) (x – 3)
= 2 (x – 3) (x – 5)
The zeros of P(x) are 3 and 5.
Sum of the zeros = 3 + 5 = 8 = −(−16)2 = -[coefficient of xcoefficient of x2]
Product of the zeros = 3 × 5 = 15 = 302 = [constant term coefficient of x2]
</header>So if ax2 + bx + c, a ≠ 0 is a quadratic polynomial and α, β are two zeros of polynomial then
α+β=−ba
αβ=ca
In general, it can be proved that if α, β, γ are the zeros of a cubic polynomial ax3 + bx2 + cx + d, then
α+β+γ=−ba
αβ+βγ+γα=ca
αβγ=−da
Note: ba, ca and da are meaningful because a ≠ 0.
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