Advertisements
Advertisements
प्रश्न
By using the method of completing the square, show that the equation `2x^2+x+4=0` has no real roots.
उत्तर
`2x^2+x+4=0`
⇒`4x^2+2x+8=0` (Multiplying both sides by 2)
⇒`4x^2+2x=-8`
⇒`(2x)^2+2xx2x xx1/2+(1/2)^2=-8+(1/2)^2` [Adding `(1/2)^2`on both sides]
⇒`(2x+1/2)^2=-8+1/4=-31/4<0`
But, `(2x+1/2)^2` cannot be negative for any real value of x.
So, there is no real value of x satisfying the given equation.
Hence, the given equation has no real roots.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by completing square method : x2 + 10x + 21 = 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.
The hypotenuse of a right-angled triangle is 1 meter less than twice the shortest side. If the third side 1 meter more than the shortest side, find the side, find the sides of the triangle.
Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares ?
Solve the following quadratic equation by completing the square method.
5x2 = 4x + 7
Fill in the gaps and complete.
Determine the nature of roots of the following quadratic equation.
x2 – 4x + 4 = 0
Sum of the roots of a quadratic equation is double their product. Find k if equation x2 – 4kx + k + 3 = 0
One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are:
Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get on the test?
