Advertisements
Advertisements
Question
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Advertisements
Solution
The given quadric equation is `kx^2-2sqrt5x+4=0`, and roots are real and equal
Then find the value of k.
Here, a = k, `b=-2sqrt5`, and c = 4
As we know that D = b2 - 4ac
Putting the value of a = k, `b=-2sqrt5`, and c = 4
`=(-2sqrt5)^2-4xxkxx4`
= 20 - 16k
The given equation will have real and equal roots, if D = 0
Thus,
20 - 16k = 0
16k = 20
k = 20/16
k = 5/4
Therefore, the value of k = 5/4.
APPEARS IN
RELATED QUESTIONS
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
The roots of the equation 7x2 + x – 1 = 0 are:
If α, β are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
The roots of quadratic equation x2 – 1 = 0 are ______.
