For a quadratic equation ax^2 + bx + c = 0,if | vedclass

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

Question

(B) For a quadratic equation $ax^2 + bx + c = 0$ with rational coefficients $a, b, c \in \mathbb{Q}$,the roots are given by the quadratic formula: $x

Vedclass · Accepted Answer

$D$ is a perfect square of a rational number and $a, b, c \in \mathbb{Q}$

Vedclass · Answer

(B) For a quadratic equation $ax^2 + bx + c = 0$ with rational coefficients $a, b, c \in \mathbb{Q}$,the roots are given by the quadratic formula: $x = \frac{-b \pm \sqrt{D}}{2a}$,where $D = b^2 - 4ac$ is the discriminant.$1$. If $D > 0$ and $D$ is a perfect square of a rational number,then $\sqrt{D}$ is rational,making the roots rational and distinct.$2$. If $D = 0$,the roots are real and equal.$3$. If $D Therefore,for the roots to be distinct and rational,$D$ must be greater than $0$ and a perfect square of a rational number,provided $a, b, c$ are rational.

For a quadratic equation $ax^2 + bx + c = 0$,if $\ldots \ldots \ldots \ldots$ then the roots are distinct and rational.

Similar Questions

The value of discriminant $D$ for the equation $(3x - 14)^2 = 0$ is ........

Which constant must be added and subtracted to solve the quadratic equation $9x^{2} + \frac{3}{4}x - \sqrt{2} = 0$ by the method of completing the square?

State whether the quadratic equation $2 x^{2}-6 x+\frac{9}{2}=0$ has two distinct real roots. Justify your answer.

Which of the following is true for the coefficients and constant term of a quadratic equation $ax^2 + bx + c = 0$?

$(x+6)(x+5)=0$ is a ....... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module