Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
Advertisements
उत्तर
x2 – 4x – 1 = 0
Here a = 1, b = -4, c = -1
∴ D = b2 - 4ac
= (-4)2 - 4 x 1 x (-1)
= 16 + 4
= 20
∵ D > 0
Roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
The quadratic equation whose one rational root is `3 + sqrt2` is
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
