Advertisements
Advertisements
प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
Determine the nature of the roots of the following quadratic equation:
2x2 - 3x + 5 = 0
Advertisements
उत्तर
Consider the equation
x2 - 3x + 5 = 0
Comparing it with ax2 + bx + c = 0, we get
a = 2, b = -3 and c = 5
Discriminant = b2 - 4ac
= (-3)2 - 4 (2) (5)
= 9 - 40
= -31
As b2 - 4ac < 0,
Therefore, no real root is possible for the given equation.
संबंधित प्रश्न
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 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 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:
`3x^2-2sqrt6x+2=0`
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
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).
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Solve the following quadratic equation using formula method only
x2 - 4x - 1 = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Every quadratic equation has at least one real root.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
