Question

Find a quadratic polynomial whose zeroes are 3 and -5. Verify the relationship between the zeroes and the coefficient of the polynomial.

Answer 1

Sum of the zeroes of the polynomial = 3+(-5) = -2 = -b/a

Product of the zeroes of the polynomial = 3(-5) = -15 = c/a

The required polynomial is k[x²-(α+β)x-αβ]

Where α and β are the roots f the polynomial

Here α=3 and β=-5

k[x²-(3+(-5))x+3(-5)]

k[x²+2x-15]

Here to simplify the polynomial

The k value must be 1

∴ The required polynomial is x²+2x-15

Sum of zeroes = -2 = -b/a = -2/1 = -2 [PROVED]

Product of the zeroes = -15 = c/a = -15/1 = -15[PROVED]

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