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Is it true that a quadratic equation with an integral coefficient has integral roots?

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True

False

answer is B.

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Detailed Solution

Given statement is that a quadratic equation with an integral coefficient has integral roots.
Let us consider an example of the equation,

8 x 2 − 2 x − 1 = 0

.
It has integral coefficients

8

- 2

and

- 1

.
Now,

8 x 2 − 2 x − 1 = 0 ⇒ 8 x 2 − 4 x + 2 x − 1 = 0 ⇒ 4 x 2 x − 1 + 1 2 x − 1 = 0 ⇒ 4 x + 1 2 x − 1 = 0

Because,

x = − 14, 12

are non-integral roots of the equation.
So, the given statement is false.
The correct statement is, a quadratic equation with integral coefficients

(0, \pm 1, \pm 2, \pm 3 \dots)

can have fractional or non-integral roots.
Hence, the correct option is 2.

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