Question

what are the relationship of zeros and coefficients for quadratic and cubic polynomials

Answer 1

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Your answer
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★ RELATION BETWEEN ZEROES AND COEFFICIENTS OF QUADRATIC POLYNOMIAL : -

General form of quadratic equation = ax² + bx + c

a, b and c are the coefficients and x is the variable.

Let , α and β be the zeroes of the quadratic polynomial.

Then ,

α + β = - (coefficient of x) / (coefficient of x²) = - b/a

α × β = constant term / coefficient of x² = c/a

Now,
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★ RELATION BETWEEN ZEROES AND COEFFICIENTS OF CUBIC POLYNOMIAL : -

General form of cubic polynomial = ax³ + bx² + cx + d

a,b,c and d are the coefficients and x I the variable .

Now,

Let , α,β and ɣ be the zeroes the cubic polynomial.

Then,

α + β + ɣ = - (coefficient of x²) / (coefficient of x³) = - b/a

αβ + βɣ + ɣα = coefficient of x / coefficient of x³ = c/a

αβɣ = constant term/coefficient of x³ = d/a

HOPE IT HELPS