`(2x-3) (3x+1)=0` - Mathematics

`(2x-3) (3x+1)=0`

⇒ (2x-3) (3x+1)=0

`⇒2x-3=0 or 3x+1=0`

`⇒2x=3 or 3x=-1`

`⇒x=3/2 or x-1/3`

Hence the roots of the given equation are` 3/2 and -1/3`

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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 5

Write the discriminant of the following quadratic equations:

(x − 1) (2x − 1) = 0

Which of the following are the roots of `3x^2+2x-1=0?`

`1/3`

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

`2x^2-2sqrt2x+1=0`

`x^2+x+2=0`

`x-1/x=3,x≠0`

`x^2-4ax-b^2+4a^2=0`

If the roots of the quadratic equation `(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0` are real and equal, show that either a=0 or `(a^3+b^3+c^3=3abc)`

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

If the quadratic equation x² + 4x + k = 0 has real and equal roots, then ______.