Download App

Quadratic Equation — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equation4 Marks
Question
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
$x^2+ 2 (m - 1) x + (m + 5) = 0.$
✓

Answer

$x^2+ 2 (m - 1) x + (m + 5) = 0$
Equating with $ax^2 + bx + c = 0$
$a = 1, b = 2 (m - 1), c = (m + 5)$
Since equation has real and equal roots.
so, $D = 0$
$\Rightarrow b^2 - 4ac = 0$
$\Rightarrow [2 (m - 1)^2 - 4 x 1 x (m + 5) = 0$
$\Rightarrow 4 (m - 1)^2 - 4 (m + 5) = 0$
$\Rightarrow 4 [m^2- 2m + 1 - m - 5)] = 0$
$\Rightarrow m^2 - 3m - 4 = 0$
$\Rightarrow (m + 1) (m - 4) = 0$
Either $m + 1 = 0$
$m = -1$
or
$m - 4 = 0$
$m = 4$
$m = -1, 4$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Quadratic Equation→Quadratic Equation — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

The volume of one sphere is $27$ times that of another sphere. Calculate the ratio of their: $(i)$ radii $(ii)$ surface areas.
→
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is $1$ and PQ is $5$ units.
→
If $x =\frac{2 m a b}{a+b}$, find the value of $\frac{x+m a}{x-m a}+\frac{x+m b}{x-m b}$
→
Nirmala went to a shop to buy a Titan watch. The cost of the watch was Rs 3,250. The rate of sales tax is 12%. The shopkeeper gave her a discount such that she got the watch for only Rs 3,248. Find the discount given by the shopkeeper.
→
The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate
The original cost of the scooter.
→
$\text{ABCD}$ is a cyclic quadrilateral. Sides $AB $ and $DC$ produced meet at point $E$ ; whereas sides $BC$ and $AD$ produced meet at point $F$. If $\angle DCF : \angle F : \angle E = 3 : 5 : 4,$ Find the angles of the cyclic quadrilateral $\text{ABCD}.$
→
Find the sum of the A.P., $14, 21, 28, …, 168.$
→
Usha sold 350 shares of Rs 150 each paying 6% dividend at Rs 120 and invested the proceeds in Rs 75 shares at par paying 8% dividend. Calculate the number of Rs 75 shares she bought and the change in her annual income.
→
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
$
→
Find the arithmetic mean $($correct to the nearest whole$-$number$)$ by using step$-$deviation method.
$x$ $5$ $10$ $15$ $20$ $25$ $30$ $35 $ $40$ $45$ $50$
$f$ $20$ $43$ $75$ $67$ $72$ $45$ $39$ $9$ $8$ $6$
→