Question

A quadratic equation with integral coefficient has integral roots. Justify your

answer.​

Answer 1

Answer:

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Answer 2

Answer:

No, the given statements is not always true consider the Quadratic equation

step-by-step explanation:

8 x ² - 2 x - 1 = 0

By splitting the middle term,

➙ 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

➙ 4 x + 1 = 0

➙ x = - 1 / 4

➙ 2 x - 1 = 0

➙ x = 1 / 2

So, the given equation has integral coefficient but no integral roots

★ Additional information:

• Before solving this question is one might start taking examples which only give integral roots, as we have done in the first example in the solution and mark the answer as true. But it is wrong. So, we need to take different types of possible equations with integral coefficients and check the roots.

• If we get an equation that doesn’t satisfy the given statement then we say that the given statement is false.