1.

Find the quadratic polynomial whose zeros are 2 and -6.Verify the relation between the coefficient and the zeros of the polynomial ​

Answer»

GIVEN:

Zeroes of polynomial are 2 and -6

TO FIND:

The QUADRATIC polynomial and verify relationship between coefficientand the zeroes

SOLUTION:

We know that,

The standard form of quadratic polynomial is,

x² - (sum of zeroes)x + product of zeroes

Sum of zeroes = α + β = 2 + (-6) = -4

Product of zeroes = αβ = 2 × -6 = -12

=> x² - (α+β)x - (αβ)

=> x² - (-4)x + (-12)

=> x² + 4x - 12

Thus, x² + 4x - 12 is the REQUIRED polynomial.

VERIFICATION:

Sum of zeroes = α + β = -b/a = -4/1 = -4

=> α + β = -4

=> -4 = -4

Product of zeroes = αβ = c/a = -12/1 = -12

=> αβ = -12

=> -12 = -12

Hence, verified!



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