Advertisements
Advertisements
प्रश्न
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
पर्याय
0 only
4
8 only
0, 8
Advertisements
उत्तर
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is 0, 8.
Explanation:
Given equation is 2x2 – kx + k = 0
On comparing with ax2 + bx + c = 0, we get
a = 2, b = –k and c = k
For equal roots, the discriminant must be zero
i.e., D = b2 – 4ac = 0
⇒ (–k)2 – 4(2)k = 0
⇒ k2 – 8k = 0
⇒ k(k – 8) = 0
∴ k = 0, 8
Hence, the required values of k are 0 and 8.
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 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 value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
Solve for x: 9x2 – 6px + (p2 – q2) = 0
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
Which of the following equations has two real and distinct roots?
