Advertisements
Advertisements
Question
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Options
6
-6
-1
1
Advertisements
Solution
Let `alpha and beta `be the roots of quadratic equation`2x^2 + kx + 4 = 0` in such a way that `alpha = 2`
Here, a = 2, b = k and , c = 4
Then , according to question sum of the roots
`alpha + beta = (-b)/a`
`2+ beta = (-k)/2`
`beta = (-k)/2 - 2`
`beta = (-k -4)/2`
And the product of the roots
`alpha .beta = c /a`
`= 4/2`
`= 2`
Putting the value of `beta = (-k -4)/2`in above
`2 xx (-k - 4)/ 2 = 2`
`(-k - 4) = 2`
` k = -4 -2`
`= -6`
Putting the value of k in `beta = (-k - 4)/2`
`beta = (-(6) - 4)/2`
`= (6-4)/2`
` = 2/2`
`beta = 1`
Therefore, value of other root be `beta = 1`
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
