Question

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

Answer 1

Given:

• We have been given the two zeroes of a quadratic polynomial, ie 2 and -6.

To Find:

• We need to find the quadratic polynomial and also Verify the relation between the coefficient and the zeros of the polynomial.

Solution:

Let 2 be α and -6 be β.

Sum of zeroes α + β = 2 + (-6) = 2 - 6 = -4

Product of zeroes αβ = 2 × (-6) = -12

We know that the the form of any quadratic polynomial is:

$k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta )$

$k( {x} {}^{2} - ( - 4x) + ( - 12))$

$k( {x}^{2} + 4x - 12)$

Hence the required polynomial is

$(x^2 + 4x - 12)$

Now, in order to verify the relation between the coefficient and the zeros of the polynomial we have,

Sum of zeroes = -b/a = -4/1 = -4.

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

Hence verified!$\green{\fcolorbox{lime}{red}{\checkmark}}$

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