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
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
Every quadratic equation has exactly one root.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
