(B) Given equation is $2x^{2} - \sqrt{5}x + 1 = 0$.On comparing with the standard form $ax^{2} + bx + c = 0$,we get:$a = 2, b = -\sqrt{5}, c = 1$.The

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(B) Given equation is $2x^{2} - \sqrt{5}x + 1 = 0$.On comparing with the standard form $ax^{2} + bx + c = 0$,we get:$a = 2, b = -\sqrt{5}, c = 1$.The discriminant $D$ is given by the formula $D = b^{2} - 4ac$.Substituting the values:$D = (-\sqrt{5})^{2} - 4(2)(1) = 5 - 8 = -3$.Since the discriminant $D < 0$,the quadratic equation has no real roots (i.e.,it has imaginary roots).

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

Medium

The quadratic equation $2x^{2} - \sqrt{5}x + 1 = 0$ has

A
two distinct real roots
B
no real roots
C
two equal real roots
D
more than $2$ real roots

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Quadratic Equations

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Mix Examples - Quadratic Equations

Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

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Medium

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The quadratic equation $2x^{2} - \sqrt{5}x + 1 = 0$ has

Similar Questions

Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $5x^{2} - 2kx + 20 = 0$.

Examine whether the following equation is quadratic or not: $16x^2 - 3 = (2x + 5)(5x - 3)$

If $x=2$ is one of the solutions of the quadratic equation $k x^{2}+3 x-4=0,$ then what is the value of $k$?

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