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write the value of the discriminant and describe the nature of its roots in the space below.
1. x^2+8x+12=0
discriminant:_____, nature of roots:___________,
2.4x^2+3x+3=0
discriminant:_____. nature of roots:____________,
3.4x^2+12x+9=0
discriminant:_____, nature of roots:___________,
4.2x^2+1=5
discriminant_____, nature of roots_____________,
5,x^2=5x+4
discriminant______, nature of roots_____________,

Respuesta :

1. [tex]x^2+8x+12=0[/tex]

discriminant: 16, nature of roots: real and unique,

2. [tex]4x^2+3x+3=0[/tex]

discriminant: -39, nature of roots: imaginary,

3. [tex]4x^2+12x+9=0[/tex]

discriminant: 0, nature of roots: real and equal,

4. [tex]2x^2+1=5[/tex]

discriminant:-32, nature of roots: imaginary,

5, [tex]x^2=5x+4[/tex]

discriminant 41, nature of roots real and unique,

For a quadratic equation [tex]ax^2+bx+c=0[/tex], the discriminant is [tex]D=b^2-4ac[/tex] and for:

[tex]D>0[/tex], roots are real and unique.

[tex]D=0[/tex], roots are real and equal.

[tex]D<0[/tex], roots are imaginary.

1. [tex]x^2+8x+12=0[/tex]

[tex]D=8^2-4(1)(12)[/tex]

[tex]D=64-48[/tex]

[tex]D=16>0[/tex]

So, roots are real and unique.

2. [tex]4x^2+3x+3=0[/tex]

[tex]D=3^2-4(4)(3)[/tex]

[tex]D=9-48[/tex]

[tex]D=-39<0[/tex]

So, roots are imaginary.

3. [tex]4x^2+12x+9=0[/tex]

[tex]D=12^2-4(4)(9)[/tex]

[tex]D=144-144[/tex]

[tex]D=0[/tex]

So, roots are real and equal.

4. [tex]2x^2+1=5[/tex]

[tex]2x^2-4=0[/tex]

[tex]D=0^2-4(2)(4)[/tex]

[tex]D=0-32[/tex]

[tex]D=-32<0[/tex]

So, roots are imaginary.

5. [tex]x^2=5x+4[/tex]

[tex]x^2-5x-4=0[/tex]

[tex]D=(-5)^2-4(1)(-4)[/tex]

[tex]D=25+16[/tex]

[tex]D=41>0[/tex]

So, roots are real and unique.

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