Advertisements
Advertisements
प्रश्न
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case.
Advertisements
उत्तर
If b2 – 4ac > 0, then the roots are real and unequal.
If b2 – 4ac < 0, then the roots are not real.
APPEARS IN
संबंधित प्रश्न
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.
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in the following equation:
kx(x – 2) + 6 = 0
Find the values of k for which the roots are real and equal in the following equation:
x2 – 4kx + k = 0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
`(2)/x^2 - (5)/x + 2` = 0
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
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 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 values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Every quadratic equation has at least one real root.
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
