The roots of the quadratic equation 2x^2 + 3x | vedclass

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

Question

(B) Given the quadratic equation $2x^2 + 3x + 1 = 0$. Comparing this with $ax^2 + bx + c = 0$,we get $a = 2, b = 3, c = 1$. The discriminant $D = b^2

Vedclass · Accepted Answer

Rational

Vedclass · Answer

(B) Given the quadratic equation $2x^2 + 3x + 1 = 0$. Comparing this with $ax^2 + bx + c = 0$,we get $a = 2, b = 3, c = 1$. The discriminant $D = b^2 - 4ac = (3)^2 - 4(2)(1) = 9 - 8 = 1$. Since $D > 0$ and $D$ is a perfect square,the roots are real and rational. Using the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$,we get $x = \frac{-3 \pm \sqrt{1}}{2(2)} = \frac{-3 \pm 1}{4}$. Thus,the roots are $x = \frac{-2}{4} = -\frac{1}{2}$ and $x = \frac{-4}{4} = -1$. Both roots are rational numbers.

The roots of the quadratic equation $2x^2 + 3x + 1 = 0$ are:

Similar Questions

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

The sum of all the real roots of the equation $|x-2|^2+|x-2|-2=0$ is

If a polynomial $x^4+x^2+1$ is divisible by $x^2+mx+1$ and $x^2+nx+1$,then $m+n$ is equal to:
$(1)$ $2$
$(2)$ $0$
$(3)$ $3$
$(4)$ $4$

The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation $6x^2 - 11x + \alpha = 0$ are rational numbers is:

The roots of the equation $(p - q)x^2 + (q - r)x + (r - p) = 0$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module