Find the zeroes of the quadratic polynomials given below. Find the sum and product of the zeroes and verify relationship to the coefficients of the terms in the polynomials.
$p (x) = x^{2} - x - 6$

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Solution

$p (x) = x^{2} - x - 6$
$= x - 3 x + 2 x - 6$
$= x (x - 3) + 2 (x - 3)$
$= (x - 3) (x + 2)$
$= (x - 3) (x + 2)$
$∴$ The value of p(x) is zero when $x = 3$ or $x = - 2$

$∴$ Sum of the Zeroes $= 3 - 2 = 1$ $= - \frac{- 1}{1} = \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}} = - \frac{b}{a}$
$∴$ Product of zeroes $= 3 \times (- 2) = - 6 = \frac{- 6}{1} = \frac{c}{a}$

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Find the zeroes of the quadratic polynomials given below. Find the sum and product of the zeroes and verify relationship to the coefficients of the terms in the polynomials.p(x)=x2−x−6

p(x)=x2−x−6=x−3x+2x−6=x(x−3)+2(x−3)=(x−3)(x+2)=(x−3)(x+2)∴ The value of p(x) is zero when x=3 or x=−2∴ Sum of the Zeroes =3−2=1 =−−11=coefficientofxcoefficientofx2=−ba∴ Product of zeroes =3×(−2)=−6=−61=ca

Find the zeroes of the quadratic polynomials given below. Find the sum and product of the zeroes and verify relationship to the coefficients of the terms in the polynomials.
$p (x) = x^{2} - x - 6$