Advertisements
Advertisements
प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Advertisements
उत्तर
The given quadratic equation is
x2 + 2x + 4 = 0
Here, a = 1, b = 2 and c = 4
Descriminant
= b2 - 4ac
= (2)2 - 4 x 1 x 4
= 4 - 16
= -12 < 0
Hence, the given equation has no real roots.
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 2x2 – 7x + 3 = 0
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + kx + 1 = -4x2 - x
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
48x² – 13x -1 = 0
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
