Question

Check 3 and -2 are Zeroes of p(x)=x↑2-x-6 are verify the relationship between the Zeroes and the coefficients.​

Answer 1

Given :

• The quadratic polynomial p(x) = x² - x - 6

To Find :

• Whether 3 and -2 are the zeros of the polynomial.

• Verify the relationship between the zeros and the coefficients.

Solution :

$\implies \sf p(x) = x^2 - x - 6$

$\implies \sf p(3) = 3^2 - 3 - 6$

$\implies \sf p(3) = 9 - 3 - 6$

$\implies \sf p(3) = 6 - 6$

$\implies \sf p(3) = 0$

Therefore 3 is a zero of the polynomial.

$\implies \sf p(x) = x^2 - x - 6$

$\implies \sf p(-2) = -2^2 - (- 2) - 6$

$\implies \sf p(-2) = 6 - 6$

$\implies \sf p (-2) = 0$

Therefore -2 is a zero of the polynomial.

VERIFICATION :

Verifying the relationship :-

Let 3 and -2 be α and β respectively.

$\implies \sf \alpha + \beta = 3 - 2 = 1 = \dfrac{- (-1)}{1} = \dfrac{- b}{a}$

$\implies \sf \alpha \times \beta = 3 \times (-2) = - 6 = \dfrac{- 6}{1} = \dfrac{c}{a}$

Hence the relationship is verified.

Answer 2

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