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3 years ago

12

n an inequality, 0.5 is the greater number. What will the position of the other number be in relation to 0.5 on the vertical num

ber line?

2 answers:

sashaice [31]3 years ago

8 0

Answer:

Step-by-step explanation:

It is equal because they both are the same

Nadya [2.5K]3 years ago

4 0

Answer:

The other number would be located below 0.5 on the vertical number line.

Step-by-step explanation:

Hoped This helped!

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Start with 1.
1st number = 1
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3 years ago

Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k

masha68 [24]

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

2

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

2

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

2

−2k−4k+12

D=k^2-6k+13D=k

2

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

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3 years ago