Solve the following quadratic equation:4x^2 + 4bx - (a^2 - b^2) =… - Vidyadip

Question

Solve the following quadratic equation:$4x^2 + 4bx - (a^2 - b^2) = 0$

✓

Answer

$4x^2 + 4bx - (a^2 - b^2) = 0\Rightarrow 4x^2 + 4bx + (b^2 - a^2) = 0$
$\Rightarrow 4x^2 + 2(b + a)x + 2(b - a)x + (b^2 - a^2) = 0$
$\Rightarrow 2x[2x + (b + a)] + (b - a)[2x + (b + a)] = 0$
$\Rightarrow [2x + (b + a)][2x + (b - a)] = 0$
$\Rightarrow 2x + (b - a) = 0 or 2x + 9b - a = 0$
$\Rightarrow\text{x}=\frac{-(\text{b}+\text{a})}{2}$ or $\text{x}=\frac{-(\text{b}-\text{a})}{2}$
$\Rightarrow\text{x}=\frac{-(\text{a}+\text{b})}{2}$ or $\text{x}=\frac{(\text{a}-\text{b})}{2}$

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 "3 Marks Question" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

A field is in the form of a circle. A fence is to be erected around the field. The cost fencing would be Rs. 2640 at the rate of Rs. 12 per metre. The, the field is to be thoroughly ploughed at the cost of Re. 0.50 per $m ^2$. What is the amount required to plough the field?
$\left[\right.$ Take $\left.\pi=\frac{22}{7}\right]$.

Solve for x and y:
3x - 5y - 19 = 0,
-7x + 3y + 1 = 0

The sum of first $q$ terms of an A.P. is $63 q-3 q^2$. If its $p^{\text {th }}$ term is -60 , find the value of $p$. Also, find the $11^{\text {th }}$ term of this A.P.

Express the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways.

An electric pole is 10m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire.

In the following, determine whether the given values are solution of the given equation or not:
$\text{x}^2-3\sqrt{3}\text{x}+6=0,$ $\text{x}=\sqrt{3},\text{x}=-2\sqrt{3}$

The perimeter of a certain sector of a circle of radius 5.6m is 27.2m. Find the area of the sector.

If $\tan\theta=\frac{4}{5},$ find the value of $\frac{\cos\theta-\sin\theta}{\cos\theta+\sin\theta}.$

A part of monthly hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for $20$ days, she has to pay $Rs.3,000$ as hostel charges whereas Mansi who takes food for $25$ days pays $Rs.3,500$ as hostel charges. Find the fixed charges and the cost of food per day.

If $S_n$ denotes the sum of the first n terms of an A.P., prove that $S_{30} = 3(S_{20} - S_{10}).$