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 equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
The roots of quadratic equation x2 – 1 = 0 are ______.
