Say true or false.
A quadratic equation with integral coefficients must have integral roots.

True

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False

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Solution

The correct option is B False
Let us take an example to prove this statement is false.
Consider the quadratic equation, ${6 x}^{2} - x - 1 = 0$
On solving this, we get
${6 x}^{2} - 3 x + 2 x - 1 = 0 3 x (2 x - 1) + 1 (2 x - 1) = 0 (3 x + 1) (2 x - 1) = 0 ⟹ x = \frac{1}{2}, \frac{- 1}{3}$

So, here we have seen that though the coefficients are integers, the roots need not be integers.

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Question 3
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.

α

β

5 x^{2} - 3 x - 1 = 0

\frac{1}{α^{2}}

\frac{1}{β^{2}}

\frac{α^{2}}{β}

\frac{β^{2}}{α}

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