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Anusha Wagle
Asked: 2022-11-04T19:06:17+05:30 In:

What is the relation between zeros and coefficient of biquadratic polynomial

What is the relation between zeros and coefficient of biquadratic polynomial
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  1. Consider quadratic polynomialP(x) = 2×2\xa0– 16x + 30.Now, 2×2\xa0– 16x + 30 = (2x – 6) (x – 3)= 2 (x – 3) (x – 5)The zeros of P(x) are 3 and 5.Sum of the zeros\xa0= 3 + 5 = 8 =\xa0−(−16)2\xa0=\xa0-[coefficient of xcoefficient of\xa0x2]Product of the zeros\xa0= 3 × 5 = 15 =\xa0302\xa0=\xa0[constant term\xa0coefficient of\xa0x2]So if ax2\xa0+ bx + c, a ≠\xa00 is a quadratic polynomial and α, β\xa0are two zeros of polynomial thenα+β=−baαβ=caIn general, it can be proved that if α, β, γ\xa0are the zeros of a cubic polynomial ax3\xa0+ bx2\xa0+ cx + d, thenα+β+γ=−baαβ+βγ+γα=caαβγ=−daNote: ba,\xa0ca\xa0and\xa0da are meaningful because a ≠\xa00.

    Like in 3x^2 + 5In this 3 is a coefficient
    Zeroes are number like a and b. Coefficient are numbers side the x and y. ?

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