Find the roots of the following quadratic equ | vedclass

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

Question

(D) To solve the quadratic equation $16 x^{2}-24 x-1=0$ by the method of completing the square,we first rewrite the equation as $16 x^{2}-24 x = 1$.Di

Vedclass · Accepted Answer

$\frac{3+\sqrt{10}}{4}$ and $\frac{3-\sqrt{10}}{4}$

Vedclass · Answer

(D) To solve the quadratic equation $16 x^{2}-24 x-1=0$ by the method of completing the square,we first rewrite the equation as $16 x^{2}-24 x = 1$.Divide the entire equation by the coefficient of $x^{2}$,which is $16$:$x^{2} - \frac{24}{16} x = \frac{1}{16}$$x^{2} - \frac{3}{2} x = \frac{1}{16}$Now,add the square of half the coefficient of $x$ to both sides. The coefficient of $x$ is $-\frac{3}{2}$,so half of it is $-\frac{3}{4}$,and its square is $\frac{9}{16}$:$x^{2} - \frac{3}{2} x + \frac{9}{16} = \frac{1}{16} + \frac{9}{16}$This simplifies to:$(x - \frac{3}{4})^{2} = \frac{10}{16}$Taking the square root of both sides:$x - \frac{3}{4} = \pm \sqrt{\frac{10}{16}}$$x - \frac{3}{4} = \pm \frac{\sqrt{10}}{4}$Solving for $x$:$x = \frac{3}{4} \pm \frac{\sqrt{10}}{4}$$x = \frac{3 \pm \sqrt{10}}{4}$Thus,the roots are $\frac{3+\sqrt{10}}{4}$ and $\frac{3-\sqrt{10}}{4}$.

Find the roots of the following quadratic equation by the method of completing the square: $16 x^{2}-24 x-1=0$

Similar Questions

If one of the roots of the equation $3x^{2} + 2kx - 3 = 0$ is $-\frac{1}{2}$,then find the value of $k$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{6}, x = 5$

Represent the following situation in the form of a quadratic equation:
The area of a rectangular plot is $528 \ m^{2}$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Find the roots of the quadratic equation using the quadratic formula:
$x^{2}+2 \sqrt{2} x-6=0$

Obtain the roots of the following quadratic equation using the quadratic formula: $\sqrt{3} x^{2} + 10 x - 8 \sqrt{3} = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module