Question
Solve the following quadratic equations by factorization:
$ 6 x^2+11 x+3=0 $
$ 6 x^2+11 x+3=0 $
✓
Answer
We have been given
$ 6 x^2+11 x+3=0 $
$ 6 x^2+9 x+2 x+3=0 $
$ 3 x(2 x+3)+1(2 x+3)=0 $
$ (2 x+3)(3 x+1)=0 $
$ 2 x+3=0$
$\text{x}=\frac{-3}{2}$
Or, $3x + 1 = 0$
$\text{x}=\frac{-1}{3}$
Hence, $\text{x}=\frac{-3}{2}$ or $\text{x}=\frac{-1}{3}$
$ 6 x^2+11 x+3=0 $
$ 6 x^2+9 x+2 x+3=0 $
$ 3 x(2 x+3)+1(2 x+3)=0 $
$ (2 x+3)(3 x+1)=0 $
$ 2 x+3=0$
$\text{x}=\frac{-3}{2}$
Or, $3x + 1 = 0$
$\text{x}=\frac{-1}{3}$
Hence, $\text{x}=\frac{-3}{2}$ or $\text{x}=\frac{-1}{3}$
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
An oil funnel of tin sheet consists of a cylindrical portion $10\ cm$ long attached to a frustum of a cone. If the total height be $22\ cm,$ the diameter of the cylindrical portion $8\ cm$ and the diameter of the top of the funnel $18\ cm,$ find the area of the tin required.
→If $A = B = 60^\circ ,$ verify that.
$\cos(\text{A}-\text{B})=\cos\text{A}\cos\text{B}+\sin\text{A}\sin\text{B}$
→$\cos(\text{A}-\text{B})=\cos\text{A}\cos\text{B}+\sin\text{A}\sin\text{B}$
If $\tan\theta=\frac{4}{5},$ find the value of $\frac{\cos\theta-\sin\theta}{\cos\theta+\sin\theta}.$
→A $16\ m$ deep well with diameter $3.5\ m$ is dug up and the earth from it is spread evenly to form a platform $27.5\ m$ by $7\ m.$ Find the height of the platform.
→Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute was recorded and summarized as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
→| Number of heartbeats per minute | $65-68$ | $68-71$ | $71-74$ | $74-77$ | $77-80$ | $80-83$ | $83-86$ |
| Number of women | $2$ | $4$ | $3$ | $8$ | $7$ | $4$ | $2$ |
In the following figure, shows a kite in which $BCD$ is the shape of a quadrant of a circle of radius $42\ cm.\ ABCD$ is a square and $= \triangle\text{CEF}$ is an isosceles right angled triangle whose equal sides are 6cm long. Find the area of the shaded region.
→A tent of height $8.25m$ is in the form of a right circular cylinder with diameter of base $30m$ and height $5.5m,$ surmounted by a right circular cone of the same base. Find the cost of the canvas of the tent at the rate of $₹\ 45\ per\ m^2$.
→Find the value of k for which the following systems of linear equations has an infinite number of solutions:
$2x + 3y = 7,$
$(k - 1)x + (k + 2)y = 3k.$
→$2x + 3y = 7,$
$(k - 1)x + (k + 2)y = 3k.$
If the lengths of the sides $BC, CA$ and $AB$ of a $\triangle\text{ABC}$ are $a, b$ and $c$ respectively and $AD$ is the bisectore of $\angle\text{A}$ then find the lengths of $BD$ and $DC.$
→Two number differ by $3$ and their product is $504.$ Find the numbers.
→