`4x^2+5x=0` - Mathematics

`4x^2+5x=0`

`4x^2+5x=0`

`⇒x(4x+5)=0`

`⇒x=0 or 4x+5=0`

`⇒x=0 or x=5-4`

Hence, the roots of the given equation are 0 and `-5/4`

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Relationship Between Discriminant and Nature of Roots

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Chapter 10: Quadratic Equations - Exercises 1

Chapter 10 Quadratic Equations
Exercises 1 | Q 6

If the roots of the equation (a² + b²) x² – 2(ac + bd) x + (c² + d²) = 0 are equal, prove that `a/b = c/d`

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

x² + x + 2 = 0

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

`sqrt3x^2+10x-8sqrt3=0`

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

3x² - 2x + 2 = 0

`2x^2+x-6=0`

`(x-1)(2x-1)=0`

`36x^2-12ax+(a^2-b^2)=0`

Find the nature of roots of the following quadratic equations:

` 3x^2-2sqrt6x+2=0`

For what values of k are the roots of the quadratic equation `3x^2+2kx+27` real and equal ?

For what values of k, the roots of the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 are equal ?