Show that if x^2 – 5x + 6 = 0, then x = 3 or x = 2 - Vidyadip

Question

Show that if $x^2 – 5x + 6 = 0$, then $x = 3$ or $x = 2$

✓

Answer

$x^{2}-5 x+6=0 \text { (given) }$
$\Rightarrow (x – 3) (x – 2) = 0 ($replacing an expression by an equal/equivalent expression$) \Rightarrow x – 3 = 0$ or $x – 2 = 0 ($from the established theorem $ab = 0 \Rightarrow $ either $a = 0 $ or $b = 0,$ for $a, b$ in $R)$
$\Rightarrow x – 3 + 3 = 0 + 3 $ or $x – 2 + 2 = 0 + 2 ($adding equal quantities on either side of the equation does not alter the nature of the equation$)$
$\Rightarrow x + 0 = 3$ or $x + 0 = 2 ($using the identity property of integers under addition$)$
$\Rightarrow x = 3$ or $x = 2 ($using the identity property of integers under addition$)$
Hence, $x^2– 5x + 6 = 0$ implies $x = 3$ or $x = 2$

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 "5 Marks Questions" from Appendix 2→Appendix 2 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find all point of discontinuity of the function $\text{f(t)}=\frac{1}{\text{t}^2+\text{t}-2},$ where $\text{t}=\frac{1}{\text{x}-1}$

Form the differential equation of the family of curves represented by the equation (a being the perimeter):$(\text{x}-\text{a})^2+2\text{y}^2=\text{a}^2$

The two adjecent sides of a parallelogram are $2\hat{\text{i}}-4\hat{\text{j}}+5\hat{\text{k}}$ and $\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}}.$ Find the unit vector parallel to one of its diagonals. Also, find its area.

Show that $\text{y}=\text{A}\cos2\text{x}+\text{B}\sin2\text{x}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+4\text{y}=0$

Differentiate the following functions with respect to x:
$(\log\text{x})^{\log\text{x}}$

If the straight line $\text{x}\cos\alpha+\text{y}\sin\alpha=\text{p}$ touches the curve $\frac{\text{x}^2}{\text{a}^2}-\frac{\text{y}^2}{\text{b}^2}=1,$ then prove that $\text{a}\cos^2\alpha-\text{b}^2\sin^2\alpha=\text{p}^2.$

If O is a point in space, ABC is a triangle and D, E, F are the mid-points of the sides BC, CA and AB respectively of the triangle, prove that $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}=\overrightarrow{\text{OD}}+\overrightarrow{\text{OE}}+\overrightarrow{\text{OF}}$.

Solve the differential equation $(1 + x^2) \frac{\text{dy}}{\text{dx}} + \text{y} = \text{e}^{\tan^{-1}\text{x}.}$

A company manufactures two types of novelty Souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours available for assembling. The profit is 50 paise each for type A and 60 paise each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two non-collinear unit vectors such that $\big|\vec{\text{a}}+\vec{\text{b}}\big|=\sqrt{3},$ find $\big(2\vec{\text{a}}-5\vec{\text{b}}\big).\big(3\vec{\text{a}}+\vec{\text{b}}\big).$