A quadratic equation with integral coefficien | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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.

Similar Questions

If the roots of the quadratic equation $5x(2x - 3) - 4 = 0$ exist,find them using the method of completing the square.

Obtain the roots of the following quadratic equation by using the quadratic formula: $9x^{2} + 7x - 2 = 0$.

Find the roots of the following quadratic equation by the method of completing the square: $x^{2}-8x+12=0$

Solve the following equation using the method of factorization: $x^{2} + (x + 5)^{2} = 625$

What is the value of $k$ if one of the roots of the quadratic equation $x^{2} + 6x + k = 0$ is $-4$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module