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

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Solution

No, a quadratic equation with integral coefficients may or may not have integral roots.
Justification
Consider the equation,
$8 x^{2} - 2 x - 1 = 0$
The roots of the given equation are $\frac{1}{2}$ and $- \frac{1}{4}$ which are not integers.
Hence, a quadratic equation with an integral coefficient might or might 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.

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