a quadratic equation with integral coefficient has integral roots. justify your answer.

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Byju's Answer Standard X Mathematics

Roots of a Quadratic Equation

A quadratic e... Question

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

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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SIMILAR QUESTIONS

Q. A quadratic equation with integral coefficient has integral roots, justify your answer.Q. Question 3

Does a quadratic equation with integral coefficient has integral roots. Justify your answer.

Q.

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

1.Every quadratic equation has at least one real root

2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots .

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.

Q. Say true or false.

A quadratic equation with integral coefficients must have integral roots.

Q. A quadratic equation with integral coefficient has two different prime numbers as its roots if the sum of the coefficients of the equation is prime, then the sum of the roots is

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Roots of a Quadratic Equation

Standard X Mathematics

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

Free solutions for Mathematics Exemplar Problems - class 10 Chapter 5 - Quadratic Equations Quadratic Equations - Exercise 4.2 question 8. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

NCERT Exemplar Solutions Class 10 Mathematics Solutions for Quadratic Equations - Exercise 4.2 in Chapter 4 - Quadratic Equations

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Write whether the following statements is true or false.

A quadratic equation with integral coefficient has integral roots.

Answer:

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.

Click here👆to get an answer to your question ✍️ 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

True

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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