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A quadratic equation with integral coefficient has integral roots. Justify your answer. Get the answer to this question and access a vast question bank that is tailored for students. Open in App Solution

No, a quadratic equation with integral coefficients may or may not have integral roots.

Justification

Consider the equation,

8x2– 2x – 1 = 0

The roots of the given equation are

12 and -14

which are not integers.

Hence, a quadratic equation with an integral coefficient might or might not have integral roots.

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Write whether the following statemensst are true or false .Justify your answers :

1.Every quadratic equation has at least one real root

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3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots .

4.A quadratic equation with integeral coeffecient has integral roots.

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A quadratic equation with integral coefficients must have integral roots.

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## Write whether the following statements is true or false A quadratic equation with integral coefficie...

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Write whether the following statements is true or false.

A quadratic equation with integral coefficient has integral roots.

No, a quadratic equation with integral coefficients may or may not have integral roots.

Justification

Consider the following equation,

8x2 – 2x – 1 = 0

The roots of the given equation are ½ and – ¼ which are not integers.

Hence, a quadratic equation with integral coefficient might or might not have integral roots.

State whether (x – √2)

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## Write whether the following statement is true or false. Justify your answer.A quadratic equation with integral coefficients has integral roots. Write whether the following statement is true or false. Justify your answer.

Question

A quadratic equation with integral coefficients has integral roots.

A

B

## False

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is B)

The given statement is false.

A quadratic education with integral coefficient can have its roots in fraction, i.e., non-integral.

For example, 5x 2 +3x−8=0 ⇒5x 2 +8x−5x−8=0 ⇒x(5x+8)−1(5x+8=0 ⇒(5x+8)(x−1)=0 ⇒5x+8=0 or (x−1)=0

Therefore, the roots are x=

5 −8 ​ and x = 1

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