###### Advertisements

###### Advertisements

Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`

###### Advertisements

#### Solution

`4x^2 + 4bx −(a^2 − b^2 )= 0`

`x^2+bx-((a^2-b^2)/4)=0`

`x^2+2(b/2)x=(a^2-b^2)/4`

`x^2+2(b/2)x+(b/2)^2=(a^2-b^2)/4+(b/2)^2`

`(x+b/2)^2=a^2/4`

`x+b/2=+-a/2`

`x=-b/2+-a/2`

`x=(-b-a)/2,(-b+a)/2`

Hence, the roots are `(-b-a)/2 and (-b+a)/2 `

#### APPEARS IN

#### RELATED QUESTIONS

Solve for x:

`16/x-1=15/(x+1);x!=0,-1`

Find the roots of the quadratic equations 2*x*^{2} + *x* + 4 = 0 by applying the quadratic formula.

Sum of the areas of two squares is 468 m^{2}. If the difference of their perimeters is 24 m, find the sides of the two squares.

Two taps running together can fill a tank in `3 1/13` hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

3x^{2} + 11x + 10 = 0

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

`x^2-(sqrt2+1)x+sqrt2=0`

`sqrt3x^2+10x+7sqrt3=0`

The sum of the areas of two squares is `640m^2` . If the difference in their perimeter be 64m, find the sides of the two square

**Solve the following quadratic equation by completing the square method.**

x^{2} + 2x – 5 = 0

**Solve the following quadratic equation by completing the square method.**

9y^{2} – 12y + 2 = 0

**Solve the following quadratic equation by completing the square method.**

m^{2} – 5m = –3

**Solve the following quadratic equation by completing the square method.**

2y^{2} + 9y + 10 = 0

Fill in the gaps and complete.

**Determine the nature of roots of the following quadratic equation.**

x^{2} – 4x + 4 = 0

**Determine the nature of roots of the following quadratic equation.**

2y^{2 }– 7y + 2 = 0

**Determine the nature of roots of the following quadratic equation.**

m^{2} + 2m + 9 = 0

**Form the quadratic equation from the roots given below.**

3 and –10

α, β are roots of *y*^{2} – 2*y* –7 = 0 find,

α^{2} + β^{2 }

α, β are roots of *y*^{2} – 2*y* –7 = 0 find,

α^{3} + β^{3 }

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares.

Complete the following activity to solve the given word problem. The Sum of squares of two consecutive even natural numbers is 244, then find those numbers.

Activity: Let the first even natural number be x

Therefore its consecutive even natural number will be = (______)

By the given condition,

x^{2} + (x + 2)^{2} = 244

x^{2} + x^{2} + 4x + 4 – (______) = 0

2x^{2} + 4x – 240 = 0

x^{2} + 2x – 120 = 0

x^{2} + (______) – (______) – 120 = 0

x(x + 12) – (______) (x + 12) = 0

(x + 12)(x – 10) = 0

x = (______)/x = 10

But natural number cannot be negative, x = – 12 is not possible.

Therefore first even natural number is x = 10.

Second even consecutive natural number = x + 2 = 10 + 2 = 12.

Find the remainder when p(x) = 3x^{2} + 2x – 7 is divided by 2x + 1.

The ratio of two numbers is 3:2 and the difference of their square is 500. Find the numbers.

Find the value of x, if `(4/7)^x (7/4)^(2x) = 343/64`.

Find the value of x, if `5^(x - 3) xx 5^(2x – 8)` = 625.