Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.
$49 x^{2} - 81$

\frac{1}{7}, \frac{- 9}{7}

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\frac{9}{7}, \frac{- 9}{7}

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\frac{3}{7}, \frac{- 9}{7}

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\frac{13}{7}, \frac{- 9}{7}

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Solution

The correct option is D $\frac{9}{7}, \frac{- 9}{7}$
$49 x^{2} - 81$
$= (7 x)^{2} - (9)^{2}$
$= (7 x + 9) (7 x - 9)$

$x = - \frac{9}{7}$ , $x = \frac{9}{7}$
The zeros of the polynomials are $- \frac{9}{7}$ , $\frac{9}{7}$

Relationship between the zeros and the coefficients of the polynomials-
Sum of the zeros=- $\frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}} = - (\frac{0}{49}) = 0$

Also sum of zeros= $- \frac{9}{7} + \frac{9}{7}$ = $\frac{- 9 + 9}{7}$ = $0$

Product of the zeros = $\frac{c o n s t a n t t e r m}{c o e f f i c i e n t o f x^{2}} = \frac{- 81}{49}$

Also the product of the zeros= $- \frac{9}{7} \times \frac{9}{7}$ = $\frac{- 81}{49}$
Hence verified.

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Similar questions

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

5 t^{2} + 12 t + 7

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

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

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

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