Question
Solve the following equations by using the method of completing the square:
$x^2 - 6x + 3 = 0$
$x^2 - 6x + 3 = 0$
✓
Answer
$x^2 - 6x + 3 = 0$
$\Rightarrow x^2 - 6x = -3$
$\Rightarrow x^2 - 2 \times x \times 3 + 3^2 = -3 + 3^2$ (Adding $3^2$ on both sides)
$\Rightarrow (x - 3)^2= -3 + 9 = 6$
$\Rightarrow\text{x}-3=\pm\sqrt6$ (Taking square root on both sides)
$\Rightarrow\text{x}-3=\sqrt6$ or $\text{x}-3=-\sqrt6$
$\Rightarrow\text{x}=3+\sqrt6$ or $\text{x}=3-\sqrt6$
Hence, $3+\sqrt6$ and $3-\sqrt6$ are the roots of the given equation.
$\Rightarrow x^2 - 6x = -3$
$\Rightarrow x^2 - 2 \times x \times 3 + 3^2 = -3 + 3^2$ (Adding $3^2$ on both sides)
$\Rightarrow (x - 3)^2= -3 + 9 = 6$
$\Rightarrow\text{x}-3=\pm\sqrt6$ (Taking square root on both sides)
$\Rightarrow\text{x}-3=\sqrt6$ or $\text{x}-3=-\sqrt6$
$\Rightarrow\text{x}=3+\sqrt6$ or $\text{x}=3-\sqrt6$
Hence, $3+\sqrt6$ and $3-\sqrt6$ are the roots of the given equation.
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
Find the zeroes of the quadratic polynomia $3 x^2-2$ and verify the relationship between the zeroes and the coefficients.
→The inner and outer radii of a hollow cylinder are $15\ cm$ and $20\ cm$, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.
→Find the median of the following frequency distribution:
→| Weekly wages $($in $₹)$ | $60-69$ | $70-79$ | $80-89$ | $90-99$ | $100-109$ | $110-119$ |
| No. of days | $5$ | $15$ | $20$ | $30$ | $20$ | $8$ |
In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?
$BL$ and $CM$ are medians of $\triangle $$ABC$ right angled at A. Prove that $4(BL^2+ CM^2) = 5BC^2$
→Check whether $–150$ is a term of the $AP: 11, 8, 5, 2, …..$
→In $\triangle\text{ABC},\text{AB}=\text{AC}.$ Side BC is produced to D. prove that
$(\text{AD}^2-\text{AC}^2)=\text{BD}.\text{CD}$
→$(\text{AD}^2-\text{AC}^2)=\text{BD}.\text{CD}$
A positive integer is of the form $3q + 1$, q being a natural number. Can you write its square in any form other than $3m + 1, 3m$ or $3m + 2$ for some integer m? Justify your answer.
→In which of the following situations, the sequence of numbers formed will form an A.P.?
Divya deposited Rs. $1000 $at compound interest at the rate of $10 \%$ per annum. The amount at the end of first year, second year, third year, ......... and so on.
→Divya deposited Rs. $1000 $at compound interest at the rate of $10 \%$ per annum. The amount at the end of first year, second year, third year, ......... and so on.
If two positive integers $p$ and $q$ are written as $p=a^2 b^3$ and $q=a^3 b,a$ and $b$ are a prime number then.Verify.$\ce{LCM} \times (p.q. ) \times \operatorname{HCF}(p.q.)=p q$
→