Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Advertisements
उत्तर
The given quadric equation is 2x2 + kx - 4 = 0, and roots are real.
Then find the value of k.
Here, a = 2, b = k and c = -4
As we know that D = b2 - 4ac
Putting the value of a = 2, b = k and c = -4
= k2 - 4 x (2) x (-4)
= k2 + 32
The given equation will have real roots, if D ≥ 0
k2 + 32
Since left hand side always positive.
So k ∈ R
APPEARS IN
संबंधित प्रश्न
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
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:
2x2 - 3x + 1 = O
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
ax2 + (4a2 - 3b)x - 12 ab = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Which of the following equations has no real roots?
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
