John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age.

(ii) The roots of the quadratic equation obtained from the given situation are:

[1 mark]

real and equal

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real and distinct

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imaginary

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cannot be found

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Solution

The correct option is B real and distinct
The equation obtained from the given situation is,
$x^{2} - 2 x - 15 = 0$
$Here, a = 1, b = - 2, c = - 15$
$Discriminant, D = b^{2} - 4 a c = (- 2)^{2} - 4 \times 1 \times (- 15) = 64 > 0$
Hence, the roots of the given equation are real and distinct.

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John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age. (ii) The roots of the quadratic equation obtained from the given situation are: [1 mark]

The correct option is B real and distinctThe equation obtained from the given situation is, x2−2x−15=0 Here, a=1,b=−2,c=−15 Discriminant, D=b2−4ac =(−2)2−4×1×(−15) =64>0 Hence, the roots of the given equation are real and distinct.

John's age was the square of his son’s age six years ago. After nine years, John's age will be twice his son's age.

(ii) The roots of the quadratic equation obtained from the given situation are:

[1 mark]

The correct option is B real and distinct
The equation obtained from the given situation is,
$x^{2} - 2 x - 15 = 0$
$Here, a = 1, b = - 2, c = - 15$
$Discriminant, D = b^{2} - 4 a c = (- 2)^{2} - 4 \times 1 \times (- 15) = 64 > 0$
Hence, the roots of the given equation are real and distinct.