Find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coefficients of the polynomial.

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Solution

Q.
Find the zeroes of the quadratic polynomial $6 x^{2} - 3 - 7 x$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Ans.
(c/a)

$6 x^{2} - 7 x - 3 = 0$

$\Rightarrow 6 x^{2} - 9 x + 2 x - 3 = 0$

$\Rightarrow 3 x (2 x - 3) + 1 (2 x - 3) = 0$

$\Rightarrow (3 x + 1) (2 x - 3) = 0$

$\Rightarrow x = \frac{- 1}{3}, \frac{3}{2}$

Now, $α + β = \frac{- 1}{3} + \frac{3}{2} = \frac{- 2 + 9}{6} = \frac{7}{6}$ and $\frac{- b}{a} = \frac{7}{6} \Rightarrow α + β = \frac{- b}{a}$

$α β = \frac{- 1}{3} \times \frac{3}{2} = \frac{- 1}{2}$ and $\frac{c}{a} = \frac{- 1}{2} \Rightarrow α β = \frac{c}{a}$

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