Advertisements
Advertisements
प्रश्न
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Advertisements
उत्तर
The given quadric equation is `x ^2 - kr + 4 = 0`, and roots are equal.
Then find the value of k.
Here, a = 1, b = -k and , c = 4
As we know that `D = b^2 - 4ac`
Putting the value of a =1,b = -k and , c = 4
=` (-k)^2 - 4 xx 1 xx 4`
=` k^2- 16`
The given equation will have equal roots, if D = 0
`k^2 - 16 = 0`
`k^2 = 16`
`k = sqrt 16`
=± 4
Therefore, the value of k =± 4 .
APPEARS IN
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
From the quadratic equation if the roots are 6 and 7.
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Solve x2/3 + x1/3 - 2 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
Equation 2x2 – 3x + 1 = 0 has ______.
