Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
Advertisements
उत्तर
The given quadric equation is 2x2 − 5x − k = 0, and roots are real
Then find the value of k.
Here,
a = 2
b = −5
c = k
As we know that D = b2 − 4ac
Putting the value of a = 2, b = −5 and c = k
= (−5)2 − 4 × (2) × (−k)
= 25 + 8k
The given equation will have real roots, if D ≥ 0
25 + 8k ≥ 0
8k ≥ −25
k ≥ `−25/8`
Therefore, the value of k ≥ `−25/8`
APPEARS IN
संबंधित प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
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.
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Prove that both the roots of the equation (x - a)(x - b) +(x - b)(x - c)+ (x - c)(x - a) = 0 are real but they are equal only when a = b = c.
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
`(2)/x^2 - (5)/x + 2` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 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.
Which of the following equations has no real roots?
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
Find the sum of the roots of the equation x2 – 8x + 2 = 0
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
