Question
Solve : 25x² + 30x + 9 = 0
✓
Answer
$\begin{array}{l}25 x^2+30 x+9=0 \text { comparing } \\ \text { the equation with } a x^2+b x+c=0 \\ \text { we get } a=25, b=30, c=9, \\ \therefore b^2-4 a c=(30)^2-4 \times 25 \times 9 \\ \qquad=900-900=0 \\ \qquad x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\ \quad=\frac{-30 \pm \sqrt{0}}{2 \times 25} \\ \therefore x=\frac{-30+0}{50} \text { or } x=\frac{-30-0}{50}\end{array}$
$\therefore \quad x=-\frac{30}{50}$ or $x=-\frac{30}{50}$
$\therefore x=-\frac{3}{5}$ or $x=-\frac{3}{5}$
that is both the roots are equal.
Also note that $25 x^2+30 x+9=0$
means $(5 x+3)^2=0$
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
A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person form the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is:
- Extremely patient.
- Extremely kind or honest.
The first term of an A.P. is p and its common difference is q. Find its $10^{th}$ term.
→The median of $19$ observations is $30$. Two more observations are made and the values of these are $8$ and $32$. Find the median of $21$ observations taken together.
→Find the values of k for which the given quadratic equation has real and distinct root:
$x^2 - kx + 9 = 0$
→$x^2 - kx + 9 = 0$
Find the coordinates of the centre of the circle passing through the points P(6,-6), Q(3,-7)and R(3,3).
In the figure 7.45, if A is the centre of the circle. ∠ PAR = 30°, AP = 7.5, find the area of the segment PQR. (π = 3.14)
A rectangular park is 100m by 50m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at $60$ paise per square metre $\big(\text{Take }\pi=3.14\big).$
→A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108cm and the diameter of the cylinder is $36\ cm$, find the cost of polishing the surface at the rate of $7$ paise per $cm^2$. $ (\text{Use}\ \pi=3.1416)$
→Find the value of k for which the following system of equations has a unique solution:
→$x + 2y = 3$
$5x + ky + 7 = 0$
Shabana's age 10 years hence, will be twice juhi's present age. 6 years back shabana's age was $\frac{5}{3}$ times Juhi's at that time find their present ages.
→