Question

(a) If fountain curve (parabola) is represented by x² + 6x + 8, then its zeros are
(i) (4, 2)
(ii) (4, -2)
(iii) (-4,2)
(iv) (-4,-2)​

Answer 1

Given  : fountain curve (parabola) is represented by x² + 6x + 8

To Find : its zeros

i) (4, 2)

(ii) (4, -2)

(iii) (-4,2)

(iv) (-4,-2)​

Solution:

x² + 6x + 8  = 0

=>  x² + 4x + 2x + 8  = 0

=>  x(x + 4) + 2(x + 4)  = 0

=> (x + 4)(x + 2) = 0

x + 4 = 0 => x = - 4

x + 2 = 0 => x = - 2

Zeroes are  -2 and - 4

(-4,-2)​

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If fountain curve (parabola) is represented by x² + 6x + 8, then its zeros are

(i) (4, 2)

(ii) (4, -2)

(iii) (-4,2)

(iv) (-4,-2)

EVALUATION

$\sf{Let \: \: f(x) = {x}^{2} + 6x + 8}$

Firstly

$\sf{f( - 2) }$

$\sf{= {( - 2)}^{2} + 6 \times ( - 2) + 8}$

$\sf{ = 4 - 12 + 8}$

$= 0$

Secondly

$\sf{ f( - 4)}$

$\sf{= {( - 4)}^{2} + 6 \times ( - 4) + 8}$

$\sf{ = 16 - 24 + 8}$

$= 0$

Hence two zeroes are - 2 & - 4

FINAL ANSWER

Hence the correct option is (iv) (-4,-2)

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