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in Quadratic Equations by (49.1k points)
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The sum of twice a whole number and three times the square of the next largest whole number is 83. What is the number ?

(a) 6

(b) 8

(c) 4

(d) –4

1 Answer

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Best answer

Correct option is (c) 4

Let the number be x.

From the given condition,

2x + 3(x + 1)2 = 83

3x2 + 8x + 3 = 83

3x2 + 8x − 80 = 0

3x2 − 12x + 20x − 80 = 0

3x(x − 4) + 20(x − 4) + 0

(3x + 20) (x − 4) = 0

Since it is an integer,

x = 4.

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