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प्रश्न
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x + 4 = 0
उत्तर
2x2 + x + 4 = 0
⇒ 2x2 + x = -4
On dividing both sides of the equation, we get
`⇒ x^2 + 1/(2x) = 2`
`⇒ x^2 + 2 × x × 1/4 = -2`
On adding (1/4)2 to both sides of the equation, we get
`⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = (1/4)^2 - 2 `
`⇒ (x + 1/4)^2 = 1/16 - 2`
`⇒ (x + 1/4)^2 = -31/16`
However, the square of number cannot be negative.
Therefore, there is no real root for the given equation
संबंधित प्रश्न
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 – 7x + 3 = 0
Two water taps together can fill a tank in `9 3/8`hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
x2 - 4ax + 4a2 - b2 = 0
`5x^2-6x-2=0`
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.
The area of right -angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters.
Find the value of discriminant.
2y2 – 5y + 10 = 0
Find the value of discriminant.
`sqrt2x^2 + 4x + 2sqrt2 = 0`
Write the value of λ for which x2 + 4x + λ is a perfect square.
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,
x2 + (x + 2)2 = 244
x2 + x2 + 4x + 4 – (______) = 0
2x2 + 4x – 240 = 0
x2 + 2x – 120 = 0
x2 + (______) – (______) – 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.
