Advertisements
Advertisements
प्रश्न
If the roots of x² + kx + k = 0 are real and equal, what is the value of k?
विकल्प
0
4
0 or 4
2
उत्तर
0 or 4
X^2+kx+k has distinct real solution .
So, for distinct real solution
Use formula b^2 - 4ac>0
a = 1 , b= k , c = k
Put formula b^2– 4ac>0
K^2 - 4×1×k >0
K^2 - 4k>0
K(k-4)>0
K>0, k -4>0
K>0, k<4
APPEARS IN
संबंधित प्रश्न
If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find the values of (i) `α^2+β^2` (ii) `α^3+β^3`
Form the quadratic equation if the roots are 3 and 8.
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Write the roots of following quadratic equation.
(p – 5) (p + 3) = 0
To decide whether 1 is a root of quadratic equation x2 + 4x – 5 = 0 or not, complete the following activity.
Activity: When x = (______)
L.H.S. = 12 + 4(______) – 5
= 1 + 4 – 5
= (______) – 5
= ______
= R.H.S
Therefore x = 1 is a root of quadratic equation x2 + 4x – 5 = 0
Solve the following quadratic equations by formula method.
5m2 – 4m – 2 = 0
Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`
Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation
Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0.
One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.
Activity:
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = `square` in the above equation
∴ `"k"(square)^2 - 10 xx square + 3` = 0
∴ `square` – 30 + 3 = 0
∴ 9k = `square`
∴ k = `square`
If the roots of the quadratic equation x2 + 12x + a = 0 are real and equal, then find the value of a.
The value of the discriminant of the equation x2 + 6x – 15 = 0 is ______.
If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.
Since, `square` is a root of equation x2 + 5x + a = 0
∴ Put x = `square` in the equation
⇒ `square^2 + 5 xx square + a` = 0
⇒ `square + square + a` = 0
⇒ `square + a` = 0
⇒ a = `square`
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
