All categories

3 years ago

Find the discriminant of the equation. x2 + 3x - 4 = 0

Mathematics

2 answers:

geniusboy [140]3 years ago

7 0

With a standard form quadratic, we see that with the quadratic formula:

$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That the part under the radical ( $b^2-4ac$ ) can tell us many things about how the roots of this polynomial behave.

If b^2-4ac were 0, that would mean the polynomial would have one root at $\frac{-b}{2a}$ . We call that a double root at (-b/2a,0).

If the discriminant is a perfect square, we note that the radical can be reduced and this the fraction is a rational number.

If the discriminant is negative, it means it has no real roots. That's because the root of a negative number is imaginary.

The last case if is the discriminant is neither a negative or a perfect square. That means the radical cannot be reduced and we will have two irrational roots.

In this problem, we see that the discriminant is:

$3^2-4*1(-4)= \\9+16=\\25$

The answer to the problem you asked is then 25, and we can also note that this quadratic has real, rational roots.

ivann1987 [24]3 years ago

5 0

Please use " ^ " to indicate exponentiation: x^2 + 3x - 4 = 0

Here, a = 1, b = 3 and c = -4.

The formula for the discriminant is b^2 - 4(a)(c).

Substituting the given values of a, b and c, we get:

(3)^2 - 4(1)(-4)

Evaluating this, we get 9 + 16 = 25.

The discriminant is 25.

-3 plus or minus √25

Taking this further, x = ------------------------------------

-3 plus or minus 5

or: x = -------------------------------- => {-4, 1} (solutions)

You might be interested in

1-1: HOMEWORK

Paraphin [41]

I think its 0.78/1...???

3 0

2 years ago

Read 2 more answers

Describe the outlier boundaries for the data set.

denis23 [38]

Step-by-step explanation:

Who's only here for points jk, all you have to do is 34

because it's the only smallest number there

4 0

2 years ago

What is the inverse of the function g(x) = x^3/8 + 16 ?

lesya692 [45]

Answer:

$\hookrightarrow \: { \rm{f(x) = \frac{ {x}^{3} }{8} + 16}} \\$

• let f(x) be m:

${ \rm{m = \frac{ {x}^{3} }{8} + 16}} \\$

• make x the subject of the function:

${ \rm{8m = {x}^{3} + 128}} \\ \\ { \rm{ {x}^{3} = 8m - 128 }} \\ \\ { \rm{ {x}^{3} = 8(m - 16) }} \\ \\ { \rm{x = \sqrt[3]{8} \times \sqrt[3]{(m - 16)} }} \\ \\ { \rm{x = 2 \sqrt[3]{(m - 16)} }}$

• therefore:

${ \boxed{ \rm{ {f}^{ - 1} (x) = 2 {(m - 16)}^{ \frac{1}{3} } }} }\\$

6 0

2 years ago

Sandra bought 30 T-shirts at the clothing store. 20% of the T-shirts were blue and half of the T-shirts were black. How many of

insens350 [35]

So you have 20% of blue and 50% of black.
So you have 70% in total that are both blue and black.
100%- 70%= 30%
So that means 30% were neither blue or black.
Do a proportion
30/100= x/30
30 x 30= 900
900 divided by 100= 9
Answer is 9 shirts are neither blue or black

8 0

3 years ago

A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br

natima [27]

Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; $\frac{64}{100}$ = 0.64

Null hypothesis: ${H_0}:p = 0.64$

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: ${H_a}:p \ne 0.64H$

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52 stating that the supermarket brand was as good as the national brand

The sample proportion $\hat p = \frac{52}{100}$

$\hat p = 0.52$

The z - value is calculated by the formula:

$z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}$

$z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}$

$z = \dfrac{-0.12}{0.048 }}$

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

At significance level, ∝ = 0.05 ; The p-value = 0.0124

According to the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝ = 0.05

The value ${z__{0.05}}$ is obtained as:

$P\left( {\left| Z \right| \le z} \right) = 0.05$

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the first column is reached and the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area to the left of z

This implies that : $P(Z \leq -1.96)=0.05$

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50. Here, we can see that the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

5 0

2 years ago