Advertisements
Advertisements
प्रश्न
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Advertisements
उत्तर
`x^2 - 2sqrt(3)x - 1` = 0
Here `a = 1, b = -2sqrt(3), c = -1`
∴ D = b2 - 4ac
= `(-2sqrt(3))^2 - 4 xx 1 xx (-1)`
= 12 + 4
= 16
∴ D > 0
∴ Roots are real and unequal.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Which of the following equations has 2 as a root?
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
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 ______.
