Advertisements
Advertisements
प्रश्न
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Advertisements
उत्तर
Yes, consider the quadratic equation 2x2 + x – 4 = 0 with rational coefficient.
The roots of the given quadratic equation are `(-1 + sqrt(33))/4` and `(-1 - sqrt(33))/4` are irrational.
APPEARS IN
संबंधित प्रश्न
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
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:
x2 - 4kx + k = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
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
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
The quadratic equation whose roots are 1:
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Every quadratic equation has at least two roots.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
