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

False

Solution

Quadratic Equation – A quadratic equation in x is an equation that can be written in the standard form, $ax^{2} + bx + c = 0$

Where a, b and c are real numbers with $a \neq 0$

Root: If $ax^{2} + bx + c = 0$                     …..(1)

Is a quadratic equation then the values of x which satisfy equation (1) are the roots of the equation.

Let us take a quadratic equation with integral coefficient

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

compare with $ax^{2} + bx + c = 0$ where $a \neq 0$

(a=2,b=-3,c=-5)

let us find the roots of the equation

$\\x=\frac{-b+\sqrt{b^{2}-4ac}}{2a}\\ x=\frac{3 \pm \sqrt{9-4(2)(-5)}}{2 \times 2}\\ x=\frac{3 \pm \sqrt{9+40}}{4}\\ x=\frac{3+\sqrt{49}}{4}\\ x=\frac{3+7}{4}=\frac{5}{7} \; \; \; \; \; \; \; \; x=\frac{3-7}{4}=-1$

Here we found that 5/2 is not on integral

Hence the given statement is false