Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Advertisements
उत्तर
x2 - 4x + 1 = 0
Here, a = 1, b = -4 and c = 1
D = b2 - 4ac
⇒ 16 - 4 x 1 x 1
⇒ 16 - 4
= 12 > 0
The given equation has real roots.
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
The roots of the equation 7x2 + x – 1 = 0 are:
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
