Advertisements
Advertisements
प्रश्न
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
विकल्प
two distinct real roots
two equal real roots
no real roots
more than two real roots
Advertisements
उत्तर
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has no real roots.
Explanation:
Given equation is `2x^2 - sqrt(5)x + 1` = 0
On comapring with ax2 + bx + c = 0, we get
a = 2, b = `-sqrt(5)` and c = 1
∴ Discriminant, D = b2 – 4ac
= `(-sqrt(5))^2 - 4 xx (2) xx (1)`
= 5 – 8
= – 3 < 0
Since, discrimant is negative,
Therefore quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has no real roots
i.e., imaginary roots.
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 quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(k + 1)x + (k + 4) = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Solve x2/3 + x1/3 - 2 = 0.
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 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.
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
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 values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
Every quadratic equations has at most two roots.
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
