Question
A quadratic equation with integral coefficient has integral roots. Justify your answer.
✓
Answer
No, a quadratic equation with integral coefficient $(0,\pm1,\pm2,\pm3\ .....)$ can have its roots in fraction, i.e., non integral.
For example, $5x^2 + 3x - 8 = 0$ has integral coefficients (coefficients $5, 3, -8$) are integrs).
Now, $5x + 3x - 8 = 0$
$\Rightarrow 5x^2 + 8x - 5x - 8 = 0$
$\Rightarrow x(5x + 8) -1(5x + 8) = 0$
$\Rightarrow (5x + 8)(x - 1) = 0$
$\Rightarrow 5x + 8 = 0 of (x - 1) = 0$
Therefore, the roots are given by $\text{x}=\frac{-8}{5}$ and $x = 1$
So, the given statement is false.
For example, $5x^2 + 3x - 8 = 0$ has integral coefficients (coefficients $5, 3, -8$) are integrs).
Now, $5x + 3x - 8 = 0$
$\Rightarrow 5x^2 + 8x - 5x - 8 = 0$
$\Rightarrow x(5x + 8) -1(5x + 8) = 0$
$\Rightarrow (5x + 8)(x - 1) = 0$
$\Rightarrow 5x + 8 = 0 of (x - 1) = 0$
Therefore, the roots are given by $\text{x}=\frac{-8}{5}$ and $x = 1$
So, the given statement is false.
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