Question
Solve the following quadratic equation:$9x^2 + 6x + 1 = 0$
✓
Answer
$9x^2 + 6x + 1 = 0$
$\Rightarrow 9x^2 + 3x + 3x + 1 = 0$
$\Rightarrow 3x(3x + 1) + 1(3x + 1) = 0$
$\Rightarrow (3x + 1)(3x + 1) = 0$
$\Rightarrow (3x + 1)^2 = 0$
$\Rightarrow 3x + 1 = 0$
$\Rightarrow\text{x}=\frac{-1}{3}$ (repeated root)
$\Rightarrow 9x^2 + 3x + 3x + 1 = 0$
$\Rightarrow 3x(3x + 1) + 1(3x + 1) = 0$
$\Rightarrow (3x + 1)(3x + 1) = 0$
$\Rightarrow (3x + 1)^2 = 0$
$\Rightarrow 3x + 1 = 0$
$\Rightarrow\text{x}=\frac{-1}{3}$ (repeated root)
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
In the given figure, side BC of $\triangle\text{ABC}$ is bisected at D and O is any point on AD. BO and CO produced meet AC and AB at E and F respectively, and AD is produced to X so that D is the midpoint of OX Prove that AO : AX = AF : AB and show that EF || BC.
→In the given figure, $\text{PSR, RTQ}$ and $\text{PAQ}$ are three semicircles of diameters $10 \ cm, 3 \ cm$ and $7 \ cm$ respectively. Find the perimeter of the shaded region. Use $\pi=3.14$
→The angles of depression of the top and bottom of 8m tall building from the top of a multistoried building are 30° and 45° respectively. Find the height of the multistoried building and the distance between the two buildings.
Prove that following numbers are irrationals:
$4+\sqrt{2}$
→$4+\sqrt{2}$
The third term of an $A.P.$ is $7$ and the seventh term exceeds three times the third term by $2$. Find the first term, the common difference and the sum of first $20$ terms.
→The difference of squares of two number is 88. If the larger number is $5$ less than twice the smaller number, then find the two numbers.
→An iron pillar consists of a cylindrical portion 2.8m high and 20cm in diameter and a cone 42cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5gm.
In $\triangle O P Q$ right angled at $P, OP = 7 $cm, $OQ - PQ = 1 cm$. Determine the values of sin $Q$ and cos $Q.$
→In a $\triangle\text{ABC}$ D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4cm, AE = 3.2cm, DE = 2cm and BC = 5cm, find BD and CE.
→If $\tan\theta=\frac{24}{7},$ find that $\sin\theta+\cos\theta.$
→