A quadratic equation with integral coefficien | vedclass

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Question

(B) The statement is false. $A$ quadratic equation with integral coefficients does not necessarily have integral roots.Consider the quadratic equation

Vedclass · Accepted Answer

False

Vedclass · Answer

(B) The statement is false. $A$ quadratic equation with integral coefficients does not necessarily have integral roots.Consider the quadratic equation $2x^2 + x - 6 = 0$, where the coefficients $2, 1, 	ext{and } -6$ are integers.Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, we get:$x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-6)}}{2(2)}$$x = \frac{-1 \pm \sqrt{1 + 48}}{4}$$x = \frac{-1 \pm \sqrt{49}}{4}$$x = \frac{-1 \pm 7}{4}$This gives two roots: $x_1 = \frac{6}{4} = 1.5$ and $x_2 = \frac{-8}{4} = -2$.Since $1.5$ is not an integer, the claim that a quadratic equation with integral coefficients must have integral roots is incorrect.

$A$ quadratic equation with integral coefficients must have integral roots. Justify your answer.

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