Question
Solve the following quadratic equation using formula method only
$15x^2 - 28 = x$
$15x^2 - 28 = x$
✓
Answer
$15 x^2-28=x $
$ 15 x^2-x-28=x$
$ a=15 ; b=-1 ; c=-28$
$D=b^2-4 a c $
$=(-1)^2-4(15)(-28) $
$=1+1680$
$ =1681$
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$ x=\frac{1 \pm \sqrt{1681}}{30} $
$x=\frac{1+41}{30}, x=\frac{1-41}{30} $
$ x=\frac{42}{30}, x=-\frac{40}{30} $
$x=\frac{7}{5} \quad, x=-\frac{4}{3}$
$ 15 x^2-x-28=x$
$ a=15 ; b=-1 ; c=-28$
$D=b^2-4 a c $
$=(-1)^2-4(15)(-28) $
$=1+1680$
$ =1681$
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$ x=\frac{1 \pm \sqrt{1681}}{30} $
$x=\frac{1+41}{30}, x=\frac{1-41}{30} $
$ x=\frac{42}{30}, x=-\frac{40}{30} $
$x=\frac{7}{5} \quad, x=-\frac{4}{3}$
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
In following fig., ABC is a right- angled triangle at A with sides $AB = 5 cm$ and $BC = 13 cm$ . A circle with centre $O$ has been inscribed in the triangle $ABC$. Calculate the radius of the incircle.
→Solve for $x: \left(x+\frac{1}{x}\right)^2-\frac{3}{2}\left(x-\frac{1}{x}\right)-4=0$
→Solve the following inequation, write the solution set and represent it on the number line:
$2 x-1 \geq x+\frac{7-x}{3}>2, x \in R .$
→$2 x-1 \geq x+\frac{7-x}{3}>2, x \in R .$
Calculate the mean of the following frequency distribution, using the step-deviation method :
| Class | 0 - 50 | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 |
| Frequency | 17 | 35 | 43 | 40 | 21 | 24 |
If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines :
P ∩ Q
P ∩ Q
Solve the following inequation and represent the solution set on the number line:
$
-3<-\frac{1}{2}-\frac{2 x}{3} \leq \frac{5}{6}, x \in R
$
→$
-3<-\frac{1}{2}-\frac{2 x}{3} \leq \frac{5}{6}, x \in R
$
State the modal class.
| Class Interval | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 | 85 - 90 |
| Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
Two circle with centres A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.
A cubical block of side $7$ cm is surmounted by a hemisphere of the largest size. Find the surfacearea of the resulting solid.
→Priyanka has a recurring deposit account of ₹ $1000$ per month at $10 \%$ per annum. If she gets ₹ $ 5550$ as interest at the time of maturity, find the total time for which the account was held.
→