The roots of the quadratic equation x^2 - 2sq | vedclass

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

Question

(C) For the quadratic equation $ax^2 + bx + c = 0$, the discriminant $D$ is given by $D = b^2 - 4ac$. Here, $a = 1$, $b = -2\sqrt{3}$, and $c = -22$.

Vedclass · Accepted Answer

real, irrational and unequal

Vedclass · Answer

(C) For the quadratic equation $ax^2 + bx + c = 0$, the discriminant $D$ is given by $D = b^2 - 4ac$. Here, $a = 1$, $b = -2\sqrt{3}$, and $c = -22$. $D = (-2\sqrt{3})^2 - 4(1)(-22) = 12 + 88 = 100$. Since $D > 0$, the roots are real and unequal. Using the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$: $x = \frac{2\sqrt{3} \pm \sqrt{100}}{2} = \frac{2\sqrt{3} \pm 10}{2} = \sqrt{3} \pm 5$. Since $\sqrt{3}$ is an irrational number, the roots $\sqrt{3} + 5$ and $\sqrt{3} - 5$ are irrational. Therefore, the roots are real, irrational, and unequal.

The roots of the quadratic equation $x^2 - 2\sqrt{3}x - 22 = 0$ are:

Similar Questions

For which real value of $a$ do the roots of the quadratic equation $2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0$ have opposite signs?

Let $\alpha, \beta$ be the roots of the quadratic equation $12x^{2}-20x+3\lambda=0$, where $\lambda \in \mathbb{Z}$. If $\frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}$, then the sum of all possible values of $\lambda$ is:

The sum of the real roots of the equation $x^4-2x^3+x-380=0$ is

The number of real solutions of the equation $e^{4x} + 4e^{3x} - 58e^{2x} + 4e^{x} + 1 = 0$ is:

If the roots of the given equation $({m^2} + 1){x^2} + 2amx + {a^2} - {b^2} = 0$ are equal,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module