Show the following quadratic equation by factorization method: x^… - Vidyadip

Question

Show the following quadratic equation by factorization method: $\text{x}^2+\text{x}+\frac{1}{\sqrt{2}}=0$

✓

Answer

$\text{x}^2+\text{x}+\frac{1}{\sqrt{2}}=0$ We will apply discriminant rule, $\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$ Where $D = b^2 - 4ac =1^2-4.1.\frac{1}{\sqrt{2}}$$= 1 - 2\sqrt{2}$
From (A) $\text{x}=\frac{-1\pm\sqrt{-(2\sqrt{2}-1})}{2}$ $=\frac{-1\pm\sqrt{2\sqrt{2}-1\text{ i}}}{2}$ Thus, $\therefore\text{x}=\frac{-1\pm\sqrt{2\sqrt{2}-1\text{ i}}}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from Quadratic Equations→Quadratic Equations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A and B be two stes such that: $\text{n(P)} = 20,$ $\text{n(A}\cup\text{B)=42 and n(A}\cap\text{B})=4.$ Find:
$\text{n(B)}.$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow\sqrt{3}}\frac{\text{x}^2-3}{{\text{x}^2+3\sqrt{3}\text{x}-12}}$

One angle of a triangle $\frac{2}{3}\text{x}$ grades and another is $\frac{3}{2}\text{x}$ degrees while the third is $\frac{\pi\text{x}}{75}$ radians. Express all the angles in degrees.

Find an infinite G.P. whose first term is 1 and each term is sum of all the terms which Follow it.

The base of an equilateral triangle with side 2a lies along the Y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

Show that the points P (–2, 3, 5), Q (1, 2, 3) and R (7, 0, –1) are collinear.

Find k so that $\lim\limits_{\text{x}\rightarrow2}\text{f(x)}$ may exist, where $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x}\le 2\\\text{x}+\text{k}, & \text{x} > 2\end{cases}.$

In a cricket team tournament 16 teams participated. A sum of ₹ 8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹ 275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?

Find k such that $\text{k}+9,\text{k}-6$ and 4 from three consecutive terms of a G.P.

Differentiate the following functions with respect to x:$\frac{2^\text{x}\cot\text{x}}{\sqrt{\text{x}}}$