Question

★ Math Problem !!

1: Find the nature of the roots of the following quadratic equations :

i ) $\boxed{\sf{\red{2x² - 3x + 5 \:=\: 0 }}}$

ii) $\boxed{\sf{\red{3x² - 4 \sqrt{3} x + 4 \:=\: 0 }}}$

2: Find the value of k for the following quadratic equations having equal roots :

i ) $\boxed{\sf{\blue{( k - 3 )x² + 6x + 9 \:=\: 0 }}}$

ii) $\boxed{\sf{\blue{2x² + 8x - k³ \:=\: 0 }}}$

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Answer 1

Answer:

)

x

2

−3x+5=0

a=2,b=−3,c=5

Discriminant, D=b

2

−4ac=9−40=−31

Since D<0, the roots are imaginary for the given equation.

ii)

3x

2

−4

3

x+4=0

a=3,b=−4

3

,c=4

Discriminant, D=b

2

−4ac=48−48=0

Since D=0, the roots are real and equal for the given equation.

3x

2

−4

3

x+4=0

a=3,b=−4

3

,c=4

x=

2a

[−b±

b

2

−4ac

]

x=

6

4

3

=

3

2

iii)

2x

2

−6x+3=0

a=2,b=−6,c=3

Discriminant, D= b

2

−4ac=36−24=12

Since D>0, roots are real but not equal.

x=

2a

[−b±

b

2

−4ac

]

x=

4

6±

12

x=

4

6±2

3

x=

2

3±

3

Answer 2

$\huge\pink{\boxed{\bold{Question}}}$

$i ) [tex]\boxed{\sf{\red{2x² - 3x + 5 \:=\: 0 }}}$

ii) $\boxed{\sf{\red{3x² - 4 \sqrt{3} x + 4 \:=\: 0 }}}$

2: Find the value of k for the following quadratic equations having equal roots :

i ) $\boxed{\sf{\blue{( k - 3 )x² + 6x + 9 \:=\: 0 }}}$

ii) $\boxed{\sf{\blue{2x² + 8x - k³ \:=\: 0 }}}$[/tex]

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