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Q.

Find a quadratic polynomial whose zeroes are 1 and -3. Verify the relation between the coefficients and zeros of the polynomial.

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a

x^{2} - 2 x - 3

b

x^{2} + 2 x - 3

c

x^{2} - 2 x + 3

d

x^{2} + 2 x + 3

answer is B.

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Detailed Solution

x = 1 and x = -3 as the roots of the quadratic polynomial.
Thus, the required polynomial is (x - 1)(x + 3)=

x^{2} + 2 x - 3

a=1, b = 2, c = -3
Sum of roots =

\frac{- b}{a}

\Rightarrow 1 + (- 3) = \frac{- 2}{1}

\Rightarrow - 2 = - 2

Product of roots =

\frac{c}{a}

\Rightarrow 1 \times (- 3) = \frac{- 3}{1} = - 3

Hence, verified.

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Find a quadratic polynomial whose zeroes are 1 and -3. Verify the relation between the coefficients and zeros of the polynomial.