Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 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 for x :
x2 + 5x − (a2 + a − 6) = 0
From the quadratic equation if the roots are 6 and 7.
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots 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 x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
