Advertisements
Advertisements
प्रश्न
Form the quadratic equation from the roots given below.
3 and –10
उत्तर
3 and –10
Sum of roots = 3 + (–10) = −7
Product of roots = 3 \[\times\]–10 = –30
The general form of the quadratic equation is \[x^2 - \left( \text{ Sum of roots } \right)x + \text{ Product of roots } = 0\]
So, the quadratic equation obtained is \[x^2 - \left( - 7 \right)x + \left( - 30 \right) = 0\]
\[x^2 + 7x - 30 = 0\]
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 – 7x + 3 = 0
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x – 4 = 0
Find the roots of the following quadratic equations, if they exist, by the method of completing the square `4x^2 + 4sqrt3x + 3 = 0`
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x + 4 = 0
Find the roots of the quadratic equations 2x2 + x + 4 = 0 by applying the quadratic formula.
Find the roots of the following equations:
`x-1/x = 3, x ≠ 0`
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.
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`
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
x2 - 4ax + 4a2 - b2 = 0
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 for x:
`4sqrt3x^2+5x-2sqrt3=0`
Solve the following quadratic equation by completing the square method.
5x2 = 4x + 7
Fill in the gaps and complete.
α, β are roots of y2 – 2y –7 = 0 find,
α3 + β3
The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is \[\frac{29}{20}\].Find the original fraction.
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. Find the scheduled duration of the flight.
Which constant should be added and subtracted to solve the quadratic equation `4"x"^2 - sqrt3"x" - 5` = 0 by the method of completing the square?
The value of `sqrt(6 + sqrt(6 + sqrt(6 ....)))`
A rectangular field has an area of 3 sq. units. The length is one more than twice the breadth ‘x’. Frame an equation to represent this.
If a, b, care in continued proportion, then show that `(a + b)^2/(ab) = (b + c)^2/(bc)`.
Since a, b, c are in continued proportion
∴ `a/b = square/square` = k(say)
⇒ b = `square`, a = `square` = `square`.k = `square`.k2
Now, L.H.S. = `(a + b)^2/(a.square) = (square + square)^2/(square*square)`
= `(squarek^2(k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
R.H.S. = `(b + c)^2/(b.square) = (square + square)^2/(square*square) = (square (k + 1)^2)/(square*square)`
= `(k + 1)^2/square`
L.H.S. = `square`
