Advertisements
Advertisements
प्रश्न
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Advertisements
उत्तर
x2 + kx + 4 = 0
Here, a = 1, b = k, c = 4
b2 - 4ac
= k2 - 4 x 1 x 4
= k2 - 16
∵ Roots are real and positive.
∴ k2 - 16 ≥ 0
⇒ k2 ≥ 16
⇒ k ≥ 4
⇒ k = 4.
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.
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
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
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
