All categories

3 years ago

Prove that the equation x^2+px-1=0 for every p has two different solutions

Mathematics

1 answer:

Sladkaya [172]3 years ago

8 0

Answer:

To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.

Consider x2+px−1=0

Discriminant D=p2−4(1)(−1)=p2+4

We know p2≥0 for all values of p

⇒p2+4≥0 (since 4>0)

Therefore D≥0

Hence the equation x2+px−1=0 has real and distinct roots for all real values of p

You might be interested in

The measure of one of the small angles of a right triangle is 14 more than 3 times the measure of the other small angle. Find th

anzhelika [568]

Step-by-step explanation:

Lets assume that angle of right angle trangles are <a,<b and <c

here one of the angle is 90°

so, <a=90°

now,

By the question

<c=3×<b+14

again,

<a+<b+<c=180° (being sum of interior angles of trangles)

90°+<b+(3×<b+14)=180° ( including the value of <a and <c)

90°+<b+3<b+14=180°

4<b=180-90-14

<b=86/4

<b=19°

<c=3×<b+14

=3×19+14

<c=71

smallest angle is 19°

and another small angle is 71°

3 0

3 years ago

What value of c makes x2 − 12x + c a perfect square trinomial? −36 −24 24 36

rewona [7]

Take half of the middle coefficient.
Then square it.

-12/2 = -6

(-6)^2 = 36

c = 36

8 0

3 years ago

Read 2 more answers

I’d really appreciate if you’d also give a brief explanation:)

ArbitrLikvidat [17]

Answer:

Only area of PQR can be calculated.

Step-by-step explanation:

In PQR, we have both the base (24 cm) and the height (15cm) which is perpendicular to the base. Therefore using these two measurements, we can take

$\frac{1}{2} \times 24 \times 15$

This is equal to 180 cm².

3 0

3 years ago

an airplane has flown 260 miles out of a total trip of 500 miles. What fraction in simplest form of the trip has been completed

solmaris [256]

260/500 = .52
.52 = 13/25
.52 = 52%

4 0

3 years ago

If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a

Karolina [17]

Let h = height of the box,
x = side length of the base.

Volume of the box is $V=x^{2} h = 115$ .
So $h = \frac{115}{ x^{2} }$

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
$S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x$
$= 2 x^{2} + \frac{460}{x}$
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

$S' = 4x- \frac{460}{ x^{2} } = 0$
$4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86$
Then $h= \frac{115}{4.86^{2}} = 4.87$
So the box is 4.86 in. wide and 4.87 in. high.

5 0

3 years ago

Read 2 more answers