Question
Solve the following equation: $2x^2 - x - 6 = 0$
✓
Answer
$2 x^2-x-6=0 $
$x^2-\frac{1}{2} x-3=0$
$x^2-2 x+\frac{3}{2} x-3=0 $
$ x(x-2)+\frac{3}{2}(x-2)=0$
$(x-2)\left(x+\frac{3}{2}\right)=0 $
$ (x-2)=0,\left(x+\frac{3}{2}\right)=0$
$x=2, x=-\frac{3}{2}$
$x^2-\frac{1}{2} x-3=0$
$x^2-2 x+\frac{3}{2} x-3=0 $
$ x(x-2)+\frac{3}{2}(x-2)=0$
$(x-2)\left(x+\frac{3}{2}\right)=0 $
$ (x-2)=0,\left(x+\frac{3}{2}\right)=0$
$x=2, x=-\frac{3}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Use a ruler and compass only in this question.
Construct the quadrilateral ABCD in which AB = 5 cm, BC = 7 cm and angle ABC = 120°, given that AC is its only line of symmetry.
Construct the quadrilateral ABCD in which AB = 5 cm, BC = 7 cm and angle ABC = 120°, given that AC is its only line of symmetry.
In the figure below, $P B$ and $Q A$ are perpendiculars to the line segment $A B$. If $P O=6 cm, Q O=9 cm$ and the area of $\triangle P O B$ $=120 cm^2$, find the area of $\triangle Q O A$.
→A manufacturing company sold an article to its distributor for ₹22000 including VAT. The distributor sold the article to a dealer for ₹22000 excluding tax and the dealer sold it to a consumer for ₹25000 plus tax (under VAT). If the rate of sales tax (under VAT) at each stage is 10%, find :
(i) the sale price of the article for the manufacturing company.
(ii) the amount of VAT paid by the dealer.
(i) the sale price of the article for the manufacturing company.
(ii) the amount of VAT paid by the dealer.
How many three digit numbers are divisible by 7?
Find the circumference of the circle whose area is $81 \pi cm ^2$.
→If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Prove that: $\sin ^6 \theta+\cos ^6 \theta=1-3 \sin ^2 \theta \cos ^2 \theta$.
→Find the ratio in which the point $R ( 1, 5)$ divides the line segment joining the points $S (-2, -1)$ and $T (5, 13).$
→Find the values of $x$ and $y$, if $\left|\begin{array}{c}3 x-y \\ 5\end{array}\right|=\left|\begin{array}{c}7 \\ x+y\end{array}\right|$
→How much money will be required to buy 400, Rs.12.50 shares at a premium of Rs.1?