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What is the relation between zeros …

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What is the relation between zeros and coefficient of biquadratic polynomial

Posted by Harsh Kushwah 4 years, 3 months ago

CBSE > Class 10 > Mathematics

3 answers

Preeti Dabral 4 years, 3 months ago

<header>

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]
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.

</header>

Armaan Armaan 4 years, 3 months ago

Like in 3x^2 + 5 In this 3 is a coefficient

Armaan Armaan 4 years, 3 months ago

Zeroes are number like a and b. Coefficient are numbers side the x and y. ?

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