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Relation between Roots and Coefficients for Quadratic

A quadratic e...

Question

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

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Solution

Step : Explanation.

Consider the quadratic equation with integral coefficient.
$8 x^{2} - 2 x - 1 = 0$
The roots of the given equation are $\frac{1}{2}$ and $\frac{1}{4}$ which are not integers.
So, quadratic equation with integral coefficient may or may not have integral roots.

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

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

Q. Question 2 (v)
Write whether the following statements are true or false. Justify your answers.
If the coefficient of

x^{2}

and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

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Relation between Roots and Coefficients for Quadratic

Standard XII Mathematics

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