Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Advertisements
उत्तर
The given quadric equation is 2kx2 - 40x + 25 = 0, and roots are real and equal
Then find the value of k.
Here, a = 2k, b = -40 and c = 25
As we know that D = b2 - 4ac
Putting the value of a = 2k, b = -40 and c = 25
= (-40)2 - 4 x (2k) x (25)
=1600 - 200k
The given equation will have real and equal roots, if D = 0
Thus,
1600 - 200k = 0
200k = 1600
k = 1600/200
k = 8
Therefore, the value of k = 8.
APPEARS IN
संबंधित प्रश्न
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Find the values of k for which the roots are real and equal in each of the following equation:
9x2 - 24x + k = 0
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
25x2 + 30x + 7 = 0
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
Which of the following equations has 2 as a root?
If a = 1, b = 4, c = – 5, then find the value of b2 – 4ac
The quadratic equation whose roots are 1:
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
Every quadratic equation has at least one real root.
