Advertisements
Advertisements
Question
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Options
two distinct real roots
two equal real roots
no real roots
more than two real roots
Advertisements
Solution
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.
RELATED QUESTIONS
Find that value of p for which the quadratic equation (p + 1)x2 − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
x2 + 4x + 5 = 0
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 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:
kx2 + 2x + 3k = 0
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
If a = 1, b = 4, c = – 5, then find the value of b2 – 4ac
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Every quadratic equations has at most two roots.
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 discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
