Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
$6 x^{2} - 3 - 7 x$

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Solution

Let $f (x) = 6 x^{2} - 3 - 7 x$
To calculate the zeros of the given equation, put $f (x) = 0$ .
$6 x^{2} - 7 x - 3 = 0$
$6 x^{2} - 9 x + 2 x - 3 = 0$
$3 x (2 x - 3) + 1 (2 x - 3) = 0$
$(3 x + 1) (2 x - 3) = 0$
$x = - \frac{1}{3}, x = \frac{3}{2}$
The zeros of the given equation is $- \frac{1}{3}$ and $\frac{3}{2}$ .
Sum of the zeros is $- \frac{1}{3} + \frac{3}{2} = \frac{7}{6}$ .
Product of the zeros is $- \frac{1}{3} \times \frac{3}{2} = - \frac{1}{2}$ .
According to the given equation
The sum of the zeros is,
$\frac{- b}{a} = \frac{- (- 7)}{6}$
$= \frac{7}{6}$
The product of the zeros is
$\frac{c}{a} = \frac{- 3}{6}$
$= - \frac{1}{2}$
Hence, it is verified that,
$s u m o f z e r o s = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}}$
And,
$p r o d u c t o f z e r o s = \frac{c o n s t a n t t e r m}{c o e f f i c i e n t o f x^{2}}$

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Question 1 (iii)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

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

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